Converting larger numbers in standard form to ordinary
Converting larger numbers in standard form to ordinary numbers is a crucial skill in science and engineering. It helps us easily work with extremely large values, like the distance between planets or the speed of light. By mastering this, you'll be able to translate massive numbers back into their full form and understand the scale of the world around you! Jump to the questions
Convert the following numbers from standard form to ordinary numbers:
Topic guide
What this worksheet practises
This worksheet provides practice on converting numbers written in standard form back into ordinary numbers. Standard form (like 4.2 × 10&sup5;) is useful for shorthand, but sometimes you need to see the full "ordinary" number to understand its true scale or to add it to another regular number.
Key method
Standard form for large numbers has a positive power. This power tells you exactly how many places the decimal point needs to move to the right.
- Look at the positive power on the 10.
- Move the decimal point that many places to the right.
- If you run out of digits while moving the decimal point, fill the empty jumps with zeroes.
- Finally, rewrite the number clearly without the decimal point (unless there are still decimal digits remaining).
Worked example
Write 6.03 × 10&sup4; as an ordinary number.
Step 1: Identify the power. The power is 4, so we need to move the decimal point 4 places to the right.
Step 2: Move the point past the '0' (1 jump) and the '3' (2 jumps). We have run out of digits.
6.03 → 603.
Step 3: We need 2 more jumps to make 4 in total. We fill these empty jumps with zeroes.
603 → 60300
The ordinary number is 60,300.
Common mistakes to avoid
The most frequent mistake is simply adding the number of zeroes indicated by the power to the end of the number. In the example above, adding four zeroes to 6.03 gives 6.030000, which is entirely wrong. The power tells you how many decimal places to move, not how many zeroes to draw.
How to check your answer
Convert your final ordinary number back into standard form in your head. If you put a decimal point after the first non-zero digit of 60300, it goes after the 6. Counting the digits after the 6 gives 4 digits. This matches the original power of 10&sup4;, confirming your answer is correct.