What does a child have to do to scale by a power of ten in the 11+?

Multiply or divide a number by 10, 100, or 1000 using place value. It is one of 55 named maths skills in the 11+, in the number strand, and this page carries 1 interactive exercise that practises it.

What is the trap in an 11+ scale by a power of ten question?

The digits change column, so counting zeros on the end of the answer is not a safe check. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.

What can I say if my child is stuck on scale by a power of ten?

Point at the next move rather than explaining the whole rule. Read what R is worth off the line, then move every digit 3 columns to the left and read the new number back.

What is not part of scale by a power of ten in the 11+?

The skill map draws the line here: Excludes arbitrary multiplication. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.

Which other 11+ skills should we practise alongside scale by a power of ten?

The number strand holds 13 skills that are tested together, and the pages next to scale by a power of ten are solve a one-step number problem, subtract whole numbers or decimals and add whole numbers or decimals. Each has its own exercise and its own link, and none of them needs an account.

How can my child practise scale by a power of ten for free?

Use Power Slider, embedded on this page. It is the exercise the skill map attaches to scale by a power of ten, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

Maths · Number

Scale by a power of ten

Multiply or divide a number by 10, 100, or 1000 using place value.

Watch the worked example

Open the video page

Power Up Place Value

This video shows how to use place value to multiply or divide a number by a power of ten. Watch an 11+ maths question solved step by step.

0:00 / 2:42

Turn on captions with the CC button. Jump to any part with the chapter buttons.

Read the transcript

Keep practising with Trace Learn. Find topics to practise next

Quick quiz: Scale by a power of ten

10 questions, with feedback after each one. No sign-up needed.

Read the questions in this quiz

Question 1
Point Q is marked on the number line. What is the value at Q divided by 100?
- A.1.35
- B.0.0135
- C.101.35
- D.0.135
Question 2
Point T is marked on the number line. What is the value at T multiplied by 10?
- A.0.0369
- B.3.69
- C.36.9
- D.0.369
Question 3
Point A is marked on the number line. What is the value at A divided by 1000?
- A.1001.54
- B.0.00154
- C.0.000154
- D.0.0154
Question 4
Point C is marked on the number line. What is the value at C divided by 100?
- A.0.165
- B.0.00165
- C.0.000165
- D.0.0165
Question 5
Point P is marked on the number line. What is the value at P divided by 100?
- A.0.00764
- B.0.000764
- C.0.764
- D.0.0764
Question 6
Point D is marked on the number line. What is the value at D multiplied by 10?
- A.1.25
- B.0.125
- C.0.0125
- D.12.5
Question 7
Point A is marked on the number line. What is the value at A divided by 1000?
- A.0.00506
- B.0.000506
- C.1005.06
- D.0.0506
Question 8
Point Q is marked on the number line. What is the value at Q multiplied by 10?
- A.17.79
- B.77.9
- C.0.779
- D.7.79
Question 9
Point A is marked on the number line. What is the value at A divided by 1000?
- A.0.000831
- B.8.31
- C.0.00831
- D.0.0831
Question 10
Point A is marked on the number line. What is the value at A divided by 1000?
- A.0.0473
- B.0.00473
- C.0.000473
- D.4.73

Practise it now

Multiply 0.166 by 1000.

Loading the interactive exercise. Nothing you do here is saved or scored.

A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Scaling by a power of ten

Point R is marked on the number line. What is the value at R multiplied by 1000?

Each small step on this line is worth 1, and every labelled tick is ten steps on.

37000
1037
370000
3700

Answer: 37000

How you get there

R sits at 37, so $37 \times 1000 = 37000$ . Each digit moves 3 columns to the left, because 1000 is 3 place-value columns worth of tens; the decimal point itself never moves.

Why the other answers tempt

The digits change column, so counting zeros on the end of the answer is not a safe check.

If they are stuck, say this

Read what R is worth off the line, then move every digit 3 columns to the left and read the new number back.

Now do it live in Power Slider

Kitchen-table script for parents

Try this together

A friendly mini script for the breakfast table, school run or a quiet two minutes. Read it aloud as written, or make it your own.

Ready? Let's try Scale by a power of ten together. Take a look at the picture. Here is what matters: Each small step on this line is worth 1, and every labelled tick is ten steps on. Here comes the question: Point R is marked on the number line. What is the value at R multiplied by 1000? A handy clue is: Read what R is worth off the line, then move every digit 3 columns to the left and read the new number back. Nice work. Here is the thinking: R sits at 37, so 37 × 1000 = 37000. Each digit moves 3 columns to the left, because 1000 is 3 place-value columns worth of tens; the decimal point itself never moves. So our answer is: 37000. One sneaky trap is: The digits change column, so counting zeros on the end of the answer is not a safe check. Can you show me the first move in your own words? No rush; one calm step is enough.

What this exercise is doing

Power Slider

Multiply 0.166 by 1000.

0.166 x $1000 = 166$ . Each column on the board is worth ten times the one to its right, so multiplying by a thousand moves every digit 3 columns to the left - and the point never budges. Any column left empty between the digits and the point is filled with a zero, because place value has no gaps.

Step 1. Slide. Multiply 0.166 by 1000 - slide the digits into place.
Step 2. Read it. Now read the board. Which number is sitting on it?

What to say if they get stuck

The decimal point is bolted to the board. It is the DIGITS that slide.
Multiplying by a thousand slides every digit 3 columns to the left.
Watch the units column as they go past - that is the digit sitting just to the left of the point at the end.

Open Power Slider on its own page to share it

Related maths skills

Add whole numbers or decimalsCalculate one addition with aligned place values.
Calculate a whole-number operationCalculate one stated addition, subtraction, multiplication, or division.
Compare and order numbersOrder or compare a bounded set of integers or decimals.
Continue a number sequenceInfer and apply one arithmetic sequence rule.
Divide whole numbers or decimalsCalculate one division and interpret any remainder as stated.
Evaluate a mixed expressionApply operation order to a supplied numerical expression.
Find a sequence termUse a stated or inferred linear rule to find a named term.
Multiply whole numbers or decimalsCalculate one multiplication using place-value reasoning or a written method.
Read place valueState the value of one digit in an integer or decimal.
Round to a stated placeRound one integer or decimal to the stated place value.
Solve a one-step number problemChoose and perform one operation in a short context.
Subtract whole numbers or decimalsCalculate one subtraction with aligned place values.

All maths 11+ skills

Questions parents ask about scale by a power of ten

What this skill involves, common mistakes and ways to practise it at home.

: Multiply or divide a number by 10, 100, or 1000 using place value. It is one of 55 named maths skills in the 11+, in the number strand, and this page carries 1 interactive exercise that practises it.
: The digits change column, so counting zeros on the end of the answer is not a safe check. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
: Point at the next move rather than explaining the whole rule. Read what R is worth off the line, then move every digit 3 columns to the left and read the new number back.
: The skill map draws the line here: Excludes arbitrary multiplication. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
: The number strand holds 13 skills that are tested together, and the pages next to scale by a power of ten are solve a one-step number problem, subtract whole numbers or decimals and add whole numbers or decimals. Each has its own exercise and its own link, and none of them needs an account.
: Use Power Slider, embedded on this page. It is the exercise the skill map attaches to scale by a power of ten, it runs in the browser with no account to make, these exercises are not scored and do not save learner records. The separate quiz sends answers for marking and shows a score, without saving an assessment record. It also has its own link, so you can send it to a child without sending them anywhere else first.

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