Small steps • strong foundations

Shift the digits.
Power up place value.

See exactly what changes when you multiply or divide whole numbers and decimals by 10, 100 or 1,000. Build the idea, try it safely, then show what you know.

✓ Uses ones ✓ No timer ✓ Helpful hints

2 shifts left

100 times as great

Place value scanner

3.4 × 100 = 340

The decimal point stays fixed. The digits change columns.

Quick guide

Make the shift make sense.

Four short stops. Say the bold ideas aloud if it helps.

1 of 4

Stop 1

Every digit has an address.

A digit's column tells us its value. The digit 6 can mean 6 hundreds, 6 tens, 6 ones or 6 tenths.

In 364, the 6 is in the tens column, so its value is 60.

Read across the chart

Look at 36.4. Each step left is 10 times the value. Each step right is one tenth of the value.

Keep saying the column names: tens, ones, tenths. The decimal point separates whole-number places from decimal places.

Stop 2

Multiplying shifts digits left.

×10 is one left shift. ×100 is two left shifts. ×1,000 is three left shifts.

4.2 × 100 = 420
Each digit is worth 100 times as much.

Do not use “just add zeros”. That breaks when decimals appear. The decimal point stays fixed.

Watch two left shifts

The 4 moves from ones to hundreds. The 2 moves from tenths to tens. A zero holds the ones place.

Stop 3

Dividing shifts digits right.

÷10 is one right shift. ÷100 is two right shifts. ÷1,000 is three right shifts.

7 ÷ 1,000 = 0.007
Each digit is worth one thousandth as much.

The zeros are placeholders. They keep the 7 in the thousandths column.

Watch three right shifts

The decimal point has not travelled. The digit 7 has moved from ones to thousandths.

1

Predict

Will the answer be greater or smaller? For a positive number, multiplying makes it greater and dividing makes it smaller.

Check the direction.

2

Count

Count the zeros in 10, 100 or 1,000. That tells you the number of place-value shifts.

1, 2 or 3 shifts.

3

Place

Move every digit to its new column. Use zero placeholders where a place would otherwise be empty.

The decimal point stays fixed.

Ready phrase: “Direction, shifts, place.” Use it whenever you feel stuck.

Place Value Lab

Choose it. Shift it. Explain it.

There is no score here. Change one thing at a time and notice what happens.

Safe practice

Live place value chart

3.6×100=?

Predict first: the answer will be greater because you are multiplying.

Press Show the shift when you are ready.

Build your Power Check

Choose the place-value shifts that are right for you today. You can select one power of 10 or combine them.

1. Choose the power of 10

Start with one shift. Add the others when that feels secure.

2. Choose the number level

Your check will focus on × and ÷ by 10 with whole-number answers.

Shift the digits.
Power up place value.

Make the shift make sense.

Every digit has an address.

Read across the chart

Multiplying shifts digits left.

Watch two left shifts

Dividing shifts digits right.

Watch three right shifts

Predict

Count

Place

Choose it. Shift it. Explain it.

Build your Power Check

Loading question…

Power check complete!

Shift the digits.Power up place value.

Make the shift make sense.

Every digit has an address.

Read across the chart

Multiplying shifts digits left.

Watch two left shifts

Dividing shifts digits right.

Watch three right shifts

Predict

Count

Place

Choose it. Shift it. Explain it.

Build your Power Check

Loading question…

Power check complete!

Shift the digits.
Power up place value.