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Standard Form: Free Printable Worksheet for Year 9
- ForYear 9
- StageKey Stage 3
- CostFree
- FormatPrintable PDF
Standard Form is a free printable maths worksheet for Year 9 (ages 13 to 14). Students write large and small numbers in standard form, and change standard form back into ordinary numbers. It takes about 15 minutes, needs only a pencil, and page 2 gives the grown-up notes, help ideas, a stretch task and the answers.
It comes from the Mini Minds Hub, the free library of printables from Jaques of London, the British games and toy company that has been making games for families since 1795. Print both pages, give page 1 to the student and keep page 2 for yourself. Black and white printing works well.
What is on the sheet
Students work through numbered questions with space to write each answer. Some questions start with a large whole number, some with a small decimal, and some with a number already in standard form that must be written out in full. The sheet includes powers of ten that are positive and negative, so students have to decide which way the decimal point moves and why.
- Write 4500 in standard form.
- Write 0.0072 in standard form.
- Write 3.2 x 10^4 as an ordinary number.
- Write 600000 in standard form.
- Write 0.5 in standard form.
- Write 8.1 x 10^-2 as an ordinary number.
- Write 25000 in standard form.
- Write 0.00031 in standard form.
A worked example
Write 530000 in standard form.
This number is different from the ones on the sheet. It shows two ways to reach the same answer.
Method 1: move the decimal point- A whole number has an invisible decimal point at the end: 530000.
- Move the point left until the first number is 1 or more but less than 10. That gives 5.3.
- The point moved 5 places, so the power of ten is 5.
- Write the number as 5.3 multiplied by a power of ten.
- 5.3 × 100000 = 530000, so the multiplier is 100000.
- 100000 is 10^5. Check by multiplying back: 5.3 × 10^5 is 530000.
Why do we use standard form?
Standard form is a way of writing a number as a value that is 1 or more but less than 10, multiplied by a power of ten. It keeps very large or very small numbers short and tidy. Long strings of zeros are easy to miscount. Standard form makes the size of a number clear at a glance, because the power of ten tells you how big or small it is.
Scientists, engineers and economists use standard form because their numbers can be huge or tiny. It also makes numbers easy to compare, since you look at the power first. Many calculators show very large and very small answers in a similar style, so knowing what the display means is a useful everyday skill.
Skills and curriculum link
- Standard form
- Powers of ten
- Place value
- Working with decimals
- Checking answers
This sheet supports the area below. It is matched to the published England framework. Please check it against your own school plan.
| Framework | Subject or area | Strand | Year |
|---|---|---|---|
| National Curriculum (England) | Maths | Number | Year 9 |
What children will be able to do
- I can write big numbers in standard form.
- I can write small numbers in standard form.
- I can change standard form back to an ordinary number.
Ideas that help with standard form
- The first numberIn standard form the first number is 1 or more but less than 10. Check this before you write the power of ten.
- The power of tenThe power says how many places the decimal point has moved. It is the size of the move, not the number of zeros you can see.
- Big and smallNumbers of 10 or more use a positive power. Numbers between 0 and 1 use a negative power. Say which one you expect before you start.
- Checking backTurn your answer back into an ordinary number. If you get the number you started with, your answer is right.
Key words
- Standard formA way of writing a number as a value that is 1 or more but less than 10, multiplied by a power of ten.
- Power of ten10 multiplied by itself a number of times. 10^3 means 10 × 10 × 10.
- IndexThe small raised number in a power. In 10^3, the index is 3. The plural is indices.
- Place valueThe value a digit has because of where it sits in a number.
- Decimal pointThe dot that separates whole numbers from parts of a whole.
- Ordinary numberA number written out in full, such as 7000, rather than in standard form.
How to use it
- Print both pages. Page 1 is for the student. Keep page 2, which has the notes and answers.
- Read the first question together. Ask the student to say whether the number is big or small before they write anything.
- Remind them that the first number must be 1 or more but less than 10. Let them choose how to find the power of ten.
- Check against page 2. Ask, "How did you know which power to use?" The reasoning matters as much as the answer.
- Come back another day and redo any questions that felt tricky. Repeating a familiar sheet builds confidence.
Help, stretch and game ideas
If it feels too hard
Count how many places the decimal point moves and use that for the power. Draw a small arrow over each jump. Big numbers move the point left, small numbers move it right. Try the first few questions first and come back to the rest later.
To stretch confident children
Multiply two numbers in standard form, such as 2 × 10^3 and 3 × 10^4. Multiply the first numbers, then work out what happens to the powers. Check by writing both as ordinary numbers. Then make up a pair of your own.
Make it a game
Race a friend. Each of you writes six ordinary numbers, big and small, then swaps papers. Race to convert them into standard form. Swap back and check each other's answers. One point for each correct answer.
Mistakes to watch for
Watch forThe first number is too big or too small, such as 62 × 10^3, so it is not in standard form.
Try thisCheck the first number is 1 or more but less than 10. Move the decimal point once more and change the power to match.
Watch forFor 120000, a child counts the zeros and writes 10^4.
Try thisCount the moves of the decimal point instead. The point starts after the last digit and must land after the 1.
Watch forA child uses a positive power for a number smaller than 1, such as 0.04.
Try thisAsk whether the number is bigger or smaller than 1. Small numbers need a negative power, so the power must show that.
Talk about it
- How can you tell if a number needs a positive or a negative power of ten?
- Why must the first number be between 1 and 10?
- Which would you rather read, a long string of zeros or standard form? Why?
- How can you check your answer by changing it back?
- How would you compare two numbers in standard form quickly?
- Where might scientists need very large or very small numbers?
Take it off the page
Card match
Write ordinary numbers on slips of paper and matching standard form answers on others. Mix them up and pair them. Make a few traps with the wrong power.
Number hunt
Look through books, an atlas or a science text for big or small numbers. Write each one in standard form and check it by changing it back.
Power of ten ladder
Draw a ladder with a power of ten on each rung, from small to large. Write an ordinary number beside each rung. Talk about how the numbers change as you climb.
Who it is for
Parents
Sit beside your child for the first question, then let them lead. About 15 minutes is plenty. If they get stuck, ask them to say whether the number is big or small, then count the moves of the decimal point.
Teachers
Use it as a starter, a plenary after teaching standard form, an early finisher task or homework. It needs no preparation beyond printing. Page 2 has support and stretch ideas for mixed ability groups and the full answers.
Home educators
Print it as part of a wider maths plan, then use it again for revision a few weeks later. Pair it with science reading where large and small numbers appear. Ask your learner to explain each answer aloud.
Where standard form fits
Before this sheet, students need confident place value, decimals and multiplying and dividing by powers of ten. Knowing that each place is ten times bigger than the one to its right makes standard form much easier to understand.
After this sheet, students can move on to calculating with numbers in standard form, and to the rules for working with powers. These ideas build through Key Stage 3 and into Key Stage 4, and they appear often in science.
Check it worked
Ask these when the sheet is finished. Listen for the reasoning, not just the answer.
- How do you know what power of ten to use?
- Why is standard form useful for very big or small numbers?
- Which of two numbers in standard form is larger, and how do you know?
Questions parents and teachers ask
- What age is Standard Form for?
It is written for Year 9 (ages 13 to 14), in Key Stage 3. It suits students who know place value and decimals and are ready to write very large and very small numbers neatly.
- What will students practise?
They practise changing ordinary numbers into standard form and changing standard form back into ordinary numbers. This includes large numbers, small decimals and positive and negative powers of ten.
- How long does it take?
It takes about 15 minutes for one student. Work through the first question together, then let them continue alone. Page 2 has ideas to make the task shorter or longer.
- What if it feels too hard?
Count how many places the decimal point moves and use that for the power. Drawing an arrow over each jump helps. Try a few questions at a time and come back to the rest another day.
- Is it free?
Yes. It is free to print for home and classroom use. You can print it again for brothers, sisters or revision, and black and white printing works well on plain A4 paper.
- Can teachers use it in class?
Yes. Teachers can use it as a starter, plenary, early finisher task, homework or table activity. It needs no preparation beyond printing, and page 2 gives support, stretch and answers.
- Is it a screen free activity?
Yes. It needs only paper and a pencil, so it works well for quiet time, homework or the holidays. Students write by hand and explain their thinking out loud.
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Made by Jaques of London, making games for families since 1795. A printable supports classroom learning and does not replace a teacher.