Place Value & Number Line

How to use it

There are three tabs at the top of the tool.

• Place value. The chart has a place for thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Tap + to add a block to a place, or type a number such as 3042.5 (up to 9999.999). The tool shows the number in digits, in words, and in expanded form, like 3000 + 40 + 2. When a place holds 10 blocks, tap Make 10 into 1 to trade them for 1 block of the next place, and watch them fly. The 1→10 button goes the other way: it breaks 1 block into 10 of the next size down, which is how you borrow when you subtract.
• Number line. Tap or drag along the line to read a number, or use the arrow keys. Tap Zoom in to open up the part of the line around your marker: 0 to 10 becomes 3 to 4, then 3.7 to 3.8, and so on. Each line you open stays above, so you can see where you came from. There are lines from 0 to 10,000 down to 0 to 1, and one from −20 to 20 for negative numbers.
• Challenges. Place it gives you a number to tap on a line, and tells you how close you were. On the easiest line, only 0, 5 and 10 are marked, so you count on from a mark you can see. Which is bigger? shows two numbers, and Round it asks you to round to the nearest 10, 100, whole number or tenth. A round is 10 questions, and you earn up to three stars.

The blocks are drawn the way real base-ten blocks look: a big cube for a thousand, a flat for a hundred, a long for a ten and a small cube for a one. For parts of a whole, a square is cut into 10 strips (tenths) or 100 small squares (hundredths), and a thousandth is a hundredth cut into 10 thin bars.

Why it works

In our number system the value of a digit depends on its place. In 3042 the 3 means 3 thousands, the 4 means 4 tens, and the 0 is a placeholder that says there are no hundreds. Each place is worth 10 times the place to its right. That is why 10 ones can be traded for 1 ten, and 10 tens for 1 hundred. The trade never changes the number, only the way it is written.

Decimals carry on the same pattern past the decimal point. A tenth is what you get when you cut a whole into 10 equal parts, and a hundredth is a tenth cut into 10 parts again. Reading 0.45 as "forty-five hundredths" or as "four tenths and five hundredths" means the same thing. It is why 0.5 is bigger than 0.45: 5 tenths is more than 4 tenths, even though 45 is a bigger number than 5. Our explainers How big is a million? and What is a fraction? go further.

In Australia we say numbers with and before the last part: "one hundred and five", "three thousand and forty-two". After the decimal point we say the digits one by one, so 3.25 is "three point two five". The tool follows these rules.

A number line shows the size of a number as a place along a line, so you can see which of two numbers is bigger, and by how much. Numbers further to the right are bigger. That makes negative numbers easier: −3 is to the right of −8, so −3 is the bigger number. Zooming in is the same idea as the decimal places: each zoom opens up a small stretch of the line and shows the next place value.

To round a number, find the two multiples on either side of it and pick the nearer one. If the number is exactly halfway, we round up, so 465 rounds to 470 and 2.5 rounds to 3.

The maths in the tool is exact. It works in whole thousandths, so 3.7 is stored as 3700, and adding, comparing and rounding never meet the tiny errors that computers sometimes make with decimals (in many programs, 0.1 + 0.2 comes out as 0.30000000000000004).

For parents and teachers

The Place Value & Number Line tool is written for Years 2 to 6. Place value, decimals and rounding are taught across the primary years, so ask your child's teacher what the class is learning. Younger children can build and trade with whole-number blocks. Older students can work with tenths, hundredths and thousandths and with the number line.

Ideas to try:

• Build the same number in two ways: type 1000, then break the thousand into 10 hundreds, then break one of those into 10 tens. Ask: Is it still 1000?
• Type 3042, then 342, then 3402. Ask what changed, and why the 0 matters.
• Try the decimals that cause trouble: 0.5 and 0.45, or 3.7 and 3.07. Which has more digits, and which is bigger?
• Read numbers aloud the Australian way, with and, and write down the expanded form.
• Use the Round it challenge before shopping, and round each price to the nearest dollar to estimate the total.

Wrong answers are used as a chance to learn. Place it lets you try again, Round it shows the two numbers on a short line, and every answer to Which is bigger? comes with the reason.

The tool works with touch, mouse and keyboard, and every button says what it does. The chart goes up to 9999.999, and the number lines go from −20 to 10,000. The only thing the tool remembers is your stars and best scores, on this device. It sends nothing anywhere.