When rounding a number, which digit do you look at, and what does it decide?

Look at the digit immediately to the right of the place you are rounding to. If that digit is 5 or more the digit you are keeping goes up by 1, and if it is less than 5 the digit you are keeping stays the same.

True or False? 1567.45 rounded to the nearest 100 is 16.

False. Every place value between the rounded digit and the decimal point has to be filled with a zero , so the answer is 1600. Leaving the zeros out changes the size of the number completely.

Why must 2.395 rounded to 2 decimal places be written as 2.40 rather than 2.4?

A value given to 2 decimal places has to show two digits after the point, so the final zero is doing real work. Writing 2.4 would claim the value is only known to 1 decimal place.

Round 4.998 to 2 decimal places.

The third decimal digit is 8, so the 9 in the second decimal place has to round up. That carry runs back through the whole number, turning 4.99 into 5.00 .

How do you find the first significant figure of a number, and why is it not always the first digit you can see?

Reading from the left, the first significant figure is the first non-zero digit. Any zeros in front of it are only holding the place value, so the first significant figure of 0.006207 is the 6 .

True or False? In the number 3097, the zero is a significant figure.

True. A zero sitting between non-zero digits is always significant, so the 0 is the second significant figure of 3097 and the 9 is the third.

Round 34 568 to 2 significant figures.

The first two significant figures are the 3 and the 4, and the digit after them is a 5, so the 4 rounds up to 5. The answer is 35 000.

Round 0.002 956 314 to 3 significant figures.

The first significant figure is the 2, so the third one is the 5, and the digit after it is a 6, which rounds the 5 up to 6. The answer is 0.002 96, with the leading zeros kept because they hold the place value.

A class of 31 students needs at least 1 adult for every 10 students. Why is the answer 4 adults and not 3.1?

A number of adults has to be a whole number , and 3 adults would only cover 30 of the students. So the calculation is rounded up , even though 3.1 would round down by the usual rule.

Why should you avoid rounding values in the middle of a calculation?

Every rounding introduces a small error, and those errors build up through the steps that follow. Keeping full values until the end, and rounding only the final answer, keeps that error out of the result.

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Rounding (SQA National 5 Maths): Flashcards

Exam code: X847 75

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FrontDecimal Places & Significant Figures
When rounding a number, which digit do you look at, and what does it decide?

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Cards in this collection (11)

When rounding a number, which digit do you look at, and what does it decide?
Look at the digit immediately to the right of the place you are rounding to.
If that digit is 5 or more the digit you are keeping goes up by 1, and if it is less than 5 the digit you are keeping stays the same.
True or False?
1567.45 rounded to the nearest 100 is 16.
False.
Every place value between the rounded digit and the decimal point has to be filled with a zero, so the answer is 1600.
Leaving the zeros out changes the size of the number completely.
Why must 2.395 rounded to 2 decimal places be written as 2.40 rather than 2.4?
A value given to 2 decimal places has to show two digits after the point, so the final zero is doing real work.
Writing 2.4 would claim the value is only known to 1 decimal place.
Round 4.998 to 2 decimal places.
The third decimal digit is 8, so the 9 in the second decimal place has to round up.
That carry runs back through the whole number, turning 4.99 into 5.00.
How do you find the first significant figure of a number, and why is it not always the first digit you can see?
Reading from the left, the first significant figure is the first non-zero digit.
Any zeros in front of it are only holding the place value, so the first significant figure of 0.006207 is the 6.
True or False?
In the number 3097, the zero is a significant figure.
True.
A zero sitting between non-zero digits is always significant, so the 0 is the second significant figure of 3097 and the 9 is the third.
Round 34 568 to 2 significant figures.
The first two significant figures are the 3 and the 4, and the digit after them is a 5, so the 4 rounds up to 5.
The answer is 35 000.
Round 0.002 956 314 to 3 significant figures.
The first significant figure is the 2, so the third one is the 5, and the digit after it is a 6, which rounds the 5 up to 6.
The answer is 0.002 96, with the leading zeros kept because they hold the place value.
Which forms of answer count as exact, rather than rounded?
A simplified fraction such as $\frac{5}{6}$ , a value left in terms of $π$ or a square root such as $4 π$ or $\sqrt{3}$ , and a decimal that terminates, such as 0.9375.
Once a value has been rounded it is no longer exact.
A class of 31 students needs at least 1 adult for every 10 students. Why is the answer 4 adults and not 3.1?
A number of adults has to be a whole number, and 3 adults would only cover 30 of the students.
So the calculation is rounded up, even though 3.1 would round down by the usual rule.
Why should you avoid rounding values in the middle of a calculation?
Every rounding introduces a small error, and those errors build up through the steps that follow.
Keeping full values until the end, and rounding only the final answer, keeps that error out of the result.

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