How to Use Place Value Blocks to Compare Decimals

A Step-by-step Guide to Using Place Value Blocks to Compare Decimals

Using place value blocks is an effective way to visually compare decimals. Here’s a step-by-step guide on how to use place value blocks to compare decimals:

Step 1: Identify the decimals:

Write down the decimal numbers you want to compare.

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Step 2: Gather place value blocks:

Obtain a set of place value blocks or base-10 blocks that represent ones (or units), tenths, hundredths, and thousandths:

• A large cube represents one whole (1 or one unit).
• A flat represents one-tenth (0.1).
• A long (or rod) represents one-hundredth (0.01).
• A small cube (or unit) represents one-thousandth (0.001).

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Step 3: Represent the decimals using place value blocks:

For each decimal number, use the appropriate place value blocks to represent the value. Arrange the blocks for each decimal number in separate groups.

Step 4: Compare the decimals visually:

Lay out the place value blocks for each decimal number side by side or one above the other, aligning them by their place values (ones, tenths, hundredths, and thousandths).

Step 5: Analyze the place value blocks:

Compare the blocks at each place value, starting with the largest place value (usually ones) and moving to the right. Determine which decimal is larger or smaller based on the number of blocks in each place value.

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Worked Example: Compare 0.35 and 0.305

1. Build 0.35: 3 flats and 5 longs.
2. Build 0.305: 3 flats, 0 longs and 5 small cubes.
3. Compare flats (tenths): 3 and 3. They tie, so move to the next block.
4. Compare longs (hundredths): 5 and 0. The first number has more.
5. So 0.35 > 0.305.

The blocks make a common mistake easy to see. 0.305 has more digits, but 5 small cubes are far less than 5 longs.

How to Add Decimals With Place Value Blocks: 0.55 + 0.29

1. Build 0.55 with 5 flats and 5 longs.
2. Build 0.29 with 2 flats and 9 longs.
3. Push them together: 7 flats and 14 longs.
4. Ten longs make one flat, so trade 10 longs for 1 flat. Now you have 8 flats and 4 longs.
5. Read the result: 8 tenths and 4 hundredths, or 0.84.

Check with the standard method: 0.55 + 0.29 = 0.84. The trade in step 4 is the same as carrying the 1 in written addition.

Try it: use blocks to find 0.38 + 0.47. (Answer: 7 flats and 15 longs, trade to 8 flats and 5 longs, so 0.85.)

Frequently Asked Questions

What are place value blocks?

Place value blocks, also called base-10 blocks, are hands-on pieces that show the size of each digit. With the large cube as 1, a flat is 0.1, a long is 0.01 and a small cube is 0.001. Each block is worth ten of the next smaller one, so students can see why 10 hundredths make 1 tenth.

How do you use place value blocks for decimals?

Choose one block to be the whole, then build each digit with the matching block. If the large cube is 1, then 0.36 is 3 flats and 6 longs. To compare two decimals, build both and compare the biggest blocks first: 0.4 (4 flats) beats 0.36 (3 flats and 6 longs) even though 0.36 has more digits.

How do you use place-value blocks to find 0.55 + 0.29?

Build 0.55 as 5 flats and 5 longs, and 0.29 as 2 flats and 9 longs. Combine them to get 7 flats and 14 longs. Trade 10 longs for 1 flat, leaving 8 flats and 4 longs. So 0.55 + 0.29 = 0.84. The trade is the same as carrying in written addition.

How do you use place-value blocks to find 1.48 − 0.83?

Build 1.48 as 1 large cube, 4 flats and 8 longs. Take away 3 longs, leaving 5 longs. You need to remove 8 flats but only have 4, so trade the large cube for 10 flats to get 14 flats. Remove 8, leaving 6 flats. The answer is 6 flats and 5 longs, or 0.65.

What decimal is shown if each small cube represents 1 hundredth?

If a small cube is 0.01, then a long (10 cubes) is 0.1 and a flat (100 cubes) is 1 whole. Count each type and write the digits in order. For example, 2 flats, 3 longs and 5 small cubes show 2.35. Always check which block is the whole before reading the number.