Convert large numbers to standard form
Converting large numbers to standard form is a way to express very big or very small numbers in a simpler format, making them easier to work with. You'll often see this used in science, engineering, and space exploration, where numbers like the distance to the nearest star or the size of a virus need to be written efficiently. Jump to the questions
Practise now
For each number, fill in the coefficient and the power of 10 in the boxes provided.
Topic guide
What this worksheet practises
This worksheet provides practice on converting ordinary large numbers into standard form (also known as scientific notation). Standard form is a shorthand way of writing very large or very small numbers, making them much easier to read, compare, and use in calculations.
Key method
A number in standard form must always be written in the format: A × 10n, where 'A' is a number between 1 and 10 (but not 10 itself), and 'n' is an integer (whole number).
- Identify the first significant figure (the first non-zero digit). Place a decimal point immediately after it to create your number 'A'.
- Count how many places the decimal point has moved from its original position (at the end of the whole number) to its new position.
- This count becomes the positive power 'n' on your 10.
Worked example
Write 45,000,000 in standard form.
Step 1: Create a number between 1 and 10 using the non-zero digits.
Place a decimal point after the 4 to get 4.5.
Step 2: Count how many places the decimal point has moved.
The point has moved from the end of 45,000,000 past seven digits to land between the 4 and the 5. So, it moved 7 places.
Step 3: Write the final answer.
4.5 × 107.
Common mistakes to avoid
A common mistake is simply counting the number of zeroes at the end of the number and using that as the power. In our example, there are six zeroes, but the power is 7 because the decimal point also had to jump past the '5'. Always count the total decimal jumps, not just the zeroes.
Things to remember
Standard form requires the first number to be strictly between 1 and 10. Writing 45 × 106 is mathematically equal to 45,000,000, but it is not correct standard form because 45 is larger than 10.