Subtracting in standard form
Subtracting in standard form involves working with numbers written as powers of 10. This skill is essential when dealing with very large or very small numbers, such as in scientific measurements or astronomy, where precision is key. By mastering subtraction in standard form, you'll be able to handle these types of calculations more easily in fields like physics and engineering. Jump to the questions
Practise now
For each question, enter the coefficient and the power of 10 in the boxes (standard form).
Topic guide
What this worksheet practises
This worksheet focuses on subtracting one standard form number from another (e.g. 8 × 10&sup5; − 3 × 10&sup4;). Similar to addition, you cannot just subtract the front numbers if the powers of 10 are not perfectly matched.
Key method
The most reliable non-calculator method is converting the numbers to ordinary form first.
- Take the first standard form number and write it out as a normal number. (Move the decimal point to the right according to the power of 10).
- Take the second standard form number and write it out as a normal number.
- Use column subtraction to take the second number away from the first. Ensure your place value columns line up exactly.
- Convert your final answer back into standard form. Ensure the front number is strictly between 1 and 9.99.
Worked example
Calculate (6 × 10&sup4;) − (8 × 10³). Give your answer in standard form.
Step 1: Convert the first number.
6 × 10&sup4; = 60,000.
Step 2: Convert the second number.
8 × 10³ = 8,000.
Step 3: Subtract them using columns.
60,000 − 8,000 = 52,000.
Step 4: Convert the answer back into standard form. The decimal point must go between the 5 and the 2.
52000 becomes 5.2 × 10&sup4;.
The final answer is 5.2 × 10&sup4;.
Common mistakes to avoid
A frequent error is assuming the power of 10 stays the same as the biggest number in the question. In the example above, the answer was indeed 5.2 × 10&sup4;. However, if the sum was (1.2 × 10&sup4;) − (8 × 10³), the normal numbers would be 12,000 − 8,000 = 4,000. Converted back, this is 4 × 10³. The power of 10 dropped from 4 down to 3. Always convert back carefully from your final normal number.
How to check your answer
When you subtract a smaller standard form number from a larger one, the final answer will usually be very close in size to the original larger number. (e.g. 60,000 minus a relatively small 8,000 leaves you with 52,000, which is still in the "tens of thousands" bracket).