True or False? 2.403 rounded to two decimal places is 2.4.

False. The rounding itself is right, but an answer given to two decimal places must show two decimal places, so it is written 2.40. The final zero is not decoration: it states the accuracy the answer is being claimed to.

Round 4.9983 to two decimal places.

The answer is 5.00. The third decimal place is 8, so you round up . Rounding 4.99 up carries through the tenths and into the units to give 5, which is written 5.00 to two decimal places.

What is the first significant figure of a number?

The first significant figure is the first non-zero digit , that is the non-zero digit with the largest place value. Zeros in front of it are only holding the place and are not significant, so the first significant figure of 0.0607 is the 6 .

True or False? The zero in 3097 is a significant figure.

True. Once you have passed the first significant figure, every digit that follows is significant, zeros included. So 0 is the second significant figure of 3097, and 9 is the third.

Round 2 530 457 to three significant figures.

The answer is 2 530 000. The first three significant figures are 2, 5 and 3, and the digit after them is 0, so they stay as they are. The zeros that follow must be kept as place holders, or the number would shrink to 253 and change size completely.

Why should you round only at the end of a calculation?

Rounding partway through throws away accuracy that the later steps still need, and the error it introduces is then carried into everything that follows. Keep at least four figures in any intermediate value, and round once, at the very end.

Why is an amount of money normally rounded to two decimal places?

The smallest unit of currency is a penny , which is one hundredth of a pound, so two decimal places is the finest an amount of money can genuinely be given to. An answer of £64.749214 is therefore written as £64.75.

What two things must you do when setting out a column addition of decimals?

Line the decimal points up in the same column, so that digits of equal place value sit above one another. Then fill any empty places with zeros , which keeps every column occupied: 2.95 + 13.2 is set out as 13.20 above 02.95.

True or False? Adding 0.2 and 0.9 needs no carrying, because both numbers are less than 1.

False. 0.2 + 0.9 = 1.1, so the tenths column overflows and a 1 must be carried into the ones column. Any column can overflow, whatever the size of the numbers, because it is the two digits in that one column that decide it.

In the column subtraction 32.50 − 1.74, the hundredths column asks for 0 − 4. What do you do?

Borrow ten hundredths from the tenths column, which turns the hundredths column into 10 − 4 = 6 and leaves 4 tenths where there were 5. The value of the number is unchanged, because the ten hundredths borrowed are worth exactly the one tenth given up.

True or False? To work out 5.32 × 4 you can find 532 × 4 first, then move the answer two places back.

True. Raising 5.32 to 532 makes it 100 times too big, so dividing the result by 100 at the end restores the correct size. That gives 532 × 4 = 2128 and then 2128 ÷ 100 = 21.28.

National 5MathsSQAApplications of MathematicsFlashcardsNumeracy SkillsCalculations

Calculations (SQA National 5 Applications of Mathematics): Flashcards

Exam code: X844 75

1/27

0Still learning

Know0

FrontMathematical Notation
Complete the sentence with the correct operations:
Finding the product of two numbers means you $______$ them, and finding the quotient means you $______$ one by the other.

Was this flashcard helpful?

Cards in this collection (27)

Complete the sentence with the correct operations:
Finding the product of two numbers means you $______$ them, and finding the quotient means you $______$ one by the other.
The completed sentence is:
Finding the product of two numbers means you multiply them, and finding the quotient means you divide one by the other.
Sum and difference are the matching words for addition and subtraction.
Define pi, $π$ .
$π$ is the ratio of the circumference of a circle to its diameter, and it has the same value for every circle.
Its decimal expansion never ends and never repeats, so it is usually approximated, most often by 3.14.
In the ratio $2 : 5$ , what does the colon tell you about the two quantities?
The colon shows a multiplicative relationship: for every 2 units of the first quantity there are 5 units of the second.
It fixes only the relative sizes of the two quantities, not their actual amounts.
True or False?
$- 5 > - 2$
False.
$- 5$ lies further left on the number line than $- 2$ , so $- 5$ is the smaller of the two numbers.
The correct statement is $- 5 < - 2$ , because the wide end of the sign always faces the larger value.
In $3^{4}$ , what does the 4 tell you to do?
The 4 is the power (also called the index), and it tells you to use 3 as a factor four times:
$3^{4} = 3 \times 3 \times 3 \times 3 = 81$
What are brackets used for in a calculation?
Brackets prioritise operations, so whatever is inside them is worked out first.
For example, $8 - (2 + 1) = 8 - 3 = 5$ , whereas working from left to right would give $8 - 2 + 1 = 7$ .
Complete the sentence about place value:
Each place value column has a value ten times $______$ than the column immediately to its $______$ in the number.
The completed sentence is:
Each place value column has a value ten times larger than the column immediately to its right in the number.
This is what makes each of the tenths, hundredths and thousandths columns one tenth of the one before it.
In the number $7.77$ , what value does each of the three 7s represent?
Reading from the left, the 7s represent 7 ones, 7 tenths and 7 hundredths:
$7.77 = 7 + 0.7 + 0.07$
The digit is the same each time, so it is the position alone that fixes the value.
True or False?
To multiply a number by 100, you add two zeros to the end of it.
False.
Multiplying by 100 increases the place value of every digit by two places, which only looks like adding two zeros when the number is a whole number.
For a decimal it fails completely: $1.45 \times 100 = 145$ , not $1.4500$ .
How can you work out $23 \times 400$ without a calculator?
Rewrite the multiple as a digit times a power of 10, here $400 = 4 \times 100$ , then multiply by each part in turn:
$23 \times 4 = 92 and 92 \times 100 = 9200$
The same split works for division, so $63 \div 7000$ becomes $63 \div 7$ and then a division by 1000.
True or False?
$68 \div 1000$ and $6.8 \div 100$ give the same answer.
True.
Both come to $0.068$ .
Going from 68 to $6.8$ already lowers every digit by one place, and dividing by 100 rather than by 1000 lowers it by one place fewer, so the two changes cancel out.
Complete the rule that decides which way you round:
You round up when the digit to the right of the required place is $______$ or more, and down when it is $______$ or less.
The completed rule is:
You round up when the digit to the right of the required place is 5 or more, and down when it is 4 or less.
The same rule works for decimal places and for significant figures, because in both cases you look at the single digit immediately after the place you are keeping.
True or False?
2.403 rounded to two decimal places is 2.4.
False.
The rounding itself is right, but an answer given to two decimal places must show two decimal places, so it is written 2.40.
The final zero is not decoration: it states the accuracy the answer is being claimed to.
Round 4.9983 to two decimal places.
The answer is 5.00.
The third decimal place is 8, so you round up.
Rounding 4.99 up carries through the tenths and into the units to give 5, which is written 5.00 to two decimal places.
What is the first significant figure of a number?
The first significant figure is the first non-zero digit, that is the non-zero digit with the largest place value.
Zeros in front of it are only holding the place and are not significant, so the first significant figure of 0.0607 is the 6.
True or False?
The zero in 3097 is a significant figure.
True.
Once you have passed the first significant figure, every digit that follows is significant, zeros included.
So 0 is the second significant figure of 3097, and 9 is the third.
Round 2 530 457 to three significant figures.
The answer is 2 530 000.
The first three significant figures are 2, 5 and 3, and the digit after them is 0, so they stay as they are.
The zeros that follow must be kept as place holders, or the number would shrink to 253 and change size completely.
Each bottle of pesticide covers 5 hectares. What is the least number of bottles needed for a farm of 82 hectares?
The answer is 17 bottles.
$82 \div 5 = 16.4$ , and 16 bottles would leave part of the farm untreated.
When a question asks for a least or minimum number, always round up, however small the decimal part is.
Why should you round only at the end of a calculation?
Rounding partway through throws away accuracy that the later steps still need, and the error it introduces is then carried into everything that follows.
Keep at least four figures in any intermediate value, and round once, at the very end.
Each cake needs 300 grams of flour. What is the greatest number of cakes that can be made from 1700 grams?
The answer is 5 cakes.
$1700 \div 300 = 5.666 . . .$ , and there is not enough flour left for a sixth cake.
When a question asks for a greatest or maximum number, always round down, however large the decimal part is.
Why is an amount of money normally rounded to two decimal places?
The smallest unit of currency is a penny, which is one hundredth of a pound, so two decimal places is the finest an amount of money can genuinely be given to.
An answer of £64.749214 is therefore written as £64.75.
What two things must you do when setting out a column addition of decimals?
Line the decimal points up in the same column, so that digits of equal place value sit above one another.
Then fill any empty places with zeros, which keeps every column occupied: 2.95 + 13.2 is set out as 13.20 above 02.95.
True or False?
Adding 0.2 and 0.9 needs no carrying, because both numbers are less than 1.
False.
0.2 + 0.9 = 1.1, so the tenths column overflows and a 1 must be carried into the ones column.
Any column can overflow, whatever the size of the numbers, because it is the two digits in that one column that decide it.
In the column subtraction 32.50 − 1.74, the hundredths column asks for 0 − 4. What do you do?
Borrow ten hundredths from the tenths column, which turns the hundredths column into 10 − 4 = 6 and leaves 4 tenths where there were 5.
The value of the number is unchanged, because the ten hundredths borrowed are worth exactly the one tenth given up.
True or False?
To work out 5.32 × 4 you can find 532 × 4 first, then move the answer two places back.
True.
Raising 5.32 to 532 makes it 100 times too big, so dividing the result by 100 at the end restores the correct size.
That gives 532 × 4 = 2128 and then 2128 ÷ 100 = 21.28.
Complete the working for the division:
$11.48 \div 7 = 1148 \div 7 \div 100 =______\div 100 =______$
The completed working is:
$11.48 \div 7 = 1148 \div 7 \div 100 = 164 \div 100 = 1.64$
A quick check: $1.64 \times 7 = 11.48$ , which is the number you started with.
How can you multiply 3.25 by 6 by splitting 3.25 into parts?
Split 3.25 by place value into 3, 0.2 and 0.05, multiply each part by 6, then add the three results:
$18 + 1.2 + 0.30 = 19.50$
Each part is easy on its own, and nothing is lost because the three parts add back to 3.25.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Next:Fractions & Percentages

More Revision Notes you might like