Powers, Roots & Standard Form (OCR GCSE Maths: Foundation): Exam Questions

i) Write $9.314\times {10}^5$ as an ordinary number.

[1]

ii) Calculate $\left(4.1\times {10}^{-3}\right)\times \left(8.9\times {10}^7\right)$
Give your answer in standard form.

[2]

Find the value of

i) $3^0,$

[1]

ii) $5^{-2}.$

[1]

Write the number 0.0605 in standard form.

Calculate $\left(1.63\times {10}^{12}\right)\times \left(2.47\times {10}^{-1}\right)$

Give your answer in standard form.

Write 45000 in standard form.

Write $2.06\times {10}^{-2}$ as an ordinary number.

[1]

i) Write down the reciprocal of 15.

[1]

ii) Write down the value of ${15}^0$.

[1]

iii) Write 0.015 in standard form.

[1]

Find the value of

$6^0+6^2$

Find the value of

5^-4

i) Write $4.2\times {10}^{-3}$ as an ordinary number.

[1]

ii) Calculate $\left(8.1\times {10}^3\right)+\left(7.9\times {10}^4\right)$ Give your answer in standard form.

[2]

Find the value of

i) $\sqrt[3]{512}$

[1]

ii) $\frac{6^8}{2^6}$

[1]

iii) 7⁰

[1]

Find the value of ${\left(\sqrt{25}\right)}^2$.

The Sun has been burning for $4.6\times {10}^9$ years.

Scientists estimate that the Sun will continue to burn for another $5\times {10}^8$ years before it becomes a red giant star.

Explain why it is appropriate to use standard form for these numbers.

Find the total time, from when the Sun started burning to when it becomes a red giant.

Give your answer in standard form.

Write ${10}^5$ as an ordinary number.

Complete this statement.

$\frac{1}{10 000}={10}^{\square }$

A grain of sand has a mass of approximately $6.4\times {10}^{-5}$ grams.

A bag of sand has a total mass of 5 kg.

Use these values to estimate the number of grains of sand in the bag.

Give your answer in standard form, correct to 2 significant figures.

You are given that

$5^{k+1}\times 25=5^7$ and ${\left(3^m\right)}^4=3^{12}$

Find the value of $k$ and the value of $m$.

i) Write $4.81\times {10}^{-3}$ as an ordinary number.

[1]

ii) Write 75000 in standard form.

[1]

iii) Calculate  $\frac{6.3\times {10}^2}{7\times {10}^{-3}}$

Write your answer in standard form.

[2]

Find the value of $x$ when $5^x\times 5^3=5^{12}$

$x=$...........................

The average distance from Earth to Mars is $2.25\times {10}^8$ km. A space ship travels from Earth to Mars at an average speed of $5.8\times {10}^4$ km/h.

Find how long, in hours, the journey takes.

.............................. hours

Find the value of  $p$ when  $5^p÷5^8=5^{13}$.

$p=$....................... 

Mercury is 58 000 000 km from the sun.

Jupiter is 7.22×10⁸ km further from the sun than Mercury.

Earth is 1.5×10⁸ km from the sun. 

Find how many times further from the sun Jupiter is, than Earth.