Converting To & From Standard Form
What is standard form and why is it used?
- Standard form is a way of writing very large and very small numbers using powers of 10
- This allows us to:
- Write them more concisely
- Compare them more easily
- Perform calculations with them more easily
How do I write a number in standard form?
- Numbers written in standard form are always written as:
- Where:
- ( is between 1 and 10)
- ( is positive) for large numbers
- ( is negative) for small numbers
- To write a large number such as 3 240 000 in standard form
- Identify the value of
- 3.24
- Find how many times you must multiply 3.24 by 10, to make 3 240 000
- Count how many places you need to move the decimal point
- We need to multiply by 10 six times
- 3 240 000 = 3.24 × 10 × 10 × 10 × 10 × 10 × 10 = 3.24 × 106
- Identify the value of
- To write a small number such as 0.000567 in standard form
- Identify the value of
- 5.67
- Find how many times you must divide 5.67 by 10, to make 0.000567
- Count how many places you need to move the decimal point
- We need to divide by 10 four times
- We are dividing rather than multiplying so the power will be negative
- 0.000567 = 5.67 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 5.67 × 10-4
- Identify the value of
Examiner Tip
- On some calculators, typing in a very large or very small number and pressing will convert it to standard form
Worked example
Standard form will be written as a × 10n where a is between 1 and 10
Find the value for a
a = 7.052
The original number is smaller than 1 so n will be negative
Count how many times you need to divide a by 10 to get the original number
0.007052 = 7.052 ÷ 10 ÷ 10 ÷ 10 (3 times)
Therefore n = -3.
0.007052 = 7.052 × 10-3
Standard form will be written as a × 10n where a is between 1 and 10
Find the value for a
a = 3.245
The original number is larger than 1 so n will be positive
Count how many times you need to multiply a by 10 to get the original number
324 500 000 = 3.245 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 (8 times)
Therefore n = 8
324 500 000 = 3.245 × 108