Writing large numbers in standard form | Maths | Quizalize & Oak National Academy

Starter quiz

A number written in __________ form represents a repeated multiplication.

exponential ✓

factorial

product

reciprocal
Which of the following are equivalent to $8000\times8000$ ?

$8\times1000\times8\times1000$ ✓

$64\times 10^6$ ✓

$6.4\times 10^7$ ✓

$6.4\times 10^6$

$64\times 10^7$
Which of the following are equivalent to $3.5\times0.03$ ?

$\frac{35\times3}{10^2}$

$\frac{35\times3}{1000}$ ✓

$\frac{35\times3}{10000}$

$\frac{35\times3}{10^3}$ ✓

$\frac{105}{10^3}$ ✓
Match each number written in exponent form with its value.

$10^4$

⇔

$10 000$ ✓

$10^5$

⇔

$100 000$ ✓

${1} \over {10^2}$

⇔

$0.01$ ✓

$10^0$

⇔

$1$ ✓

$10^1$

⇔

$10$ ✓

${1} \over {10^4}$

⇔

$0.0001$ ✓
Which of the following calculations are equivalent to 400 × 700?

4 × 100 × 7 × 100 ✓

4 × 100 × 7 × 1000

2.8 × 100 000 ✓

28 000

28 × 10 000 ✓
Without using a calculator, work out 3.4 × 2.5.

'8.5' ✓

Exit quiz

Which of the following are written in exponential form?

$2^4$ ✓

$5\times5\times5\times 5$

$3^6$ ✓

${4}^{-2}$ ✓

$(-3)\times( -3) \times( -3)$
Which of the following are written in standard form?

${2.6}\times10^{4}$ ✓

${3.9}\times10^{2}$ ✓

${24}\times10^{3}$

${1.05}\times10^{7}$ ✓

${0.48}\times10^{5}$
Write $34 000 000$ in standard form.

$34\times10^{6}$

$3.4\times10^{6}$

$0.34\times10^{8}$

$3.4\times10^{7}$ ✓

$3\times10^{7}$
Match each ordinary number to the equivalent number written in standard form.

$303 000$

⇔

${3.03}\times10^{5}$ ✓

$33 000$

⇔

${3.3}\times10^{4}$ ✓

$30 300$

⇔

${3.03}\times10^{4}$ ✓

$303$

⇔

${3.03}\times10^{2}$ ✓

$3 300 000$

⇔

${3.3}\times10^{6}$ ✓

$3300$

⇔

${3.3}\times10^{3}$ ✓
${1.8}\times10^{4}$ as an ordinary number is ______.

'18000' ✓
What is covered up on the calculator display?

$\times10^{13}$

$\times10^{14}$ ✓

$\div10^{13}$

$\times10^{15}$

$\div10^{14}$

Worksheet

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Lesson Details

Key learning points

It is difficult to read very large numbers, due to the number of digits involved.
It can be more efficient to write these very large numbers in standard form.
There is a convention for standard form.

Common misconception

Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.

Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.

Keywords

Standard form - Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).