P4 Whole Numbers to 100,000

P4 numbers stretch one place further than the P3 four-digit numbers. A digit still has a job because of its column, even when another column is zero.

Parents: ask your child to predict the rounded number before revealing the counters and number line.

By the end you will be able to represent numbers to 100,000, read their words, compare and order them, continue sequences, round to three accuracies and use the sign ≈.

Place value through 100,000

The place value of a digit tells you what it contributes. In 46,582, the 4 is worth four ten-thousands, the 6 is worth six thousands, and so on. The upper endpoint 100,000 has one hundred-thousands place; it is not a ten-thousands digit of 10.

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Place-value counters (P4)

🤔 Predict first: Starting at 9,900 and counting forward by 100, what boundary value comes next?

9,91010,00010,100

Expand 46,582

$$46,582=4\times10,000+6\times1,000+5\times100+8\times10+2$$

$$46,582=40,000+6,000+500+80+2$$

$$40,006=4\times10,000+0\times1,000+0\times100+0\times10+6$$

The zeroes in 40,006 hold the thousands, hundreds and tens columns. They stop the 6 from moving into the wrong place.

Read, compare and order

Read a numeral by grouping its places, then compare from the highest place that differs. The first different place decides the greater number. This works for one number with zero placeholders too.

Show the worked solution

Order four numbers

$$8,999<40,006<46,528<46,582$$

Order four numbers

$$\text{Compare the highest place that differs.}$$

$$\text{forty thousand and six}=40,006$$

Continue a sequence

The sequences in this lesson use the same positive step each time when increasing, or the same subtraction step when decreasing. Find the change between two neighbouring terms before filling the next term.

Show the worked solution

Keep the step

$$46,000,46,500,47,000,47,500$$

Keep the step

$$80,000,79,000,78,000,77,000$$

$$\text{The steps are +500 and -1,000.}$$

Round and estimate

To round, look at the digit immediately to the right of the place named. A digit from 5 to 9 rounds up; 0 to 4 rounds down. The rounded value is close, so use ≈ instead of = when the exact number has changed.

Three rounding targets

$$46,582\rightarrow46,580\text{ (nearest 10)}$$

$$46,582\rightarrow46,600\text{ (nearest 100)}$$

$$46,582\approx47,000\text{ (nearest 1,000)}$$

$$\text{The last line is approximate, not exact.}$$

Practise with worked steps

Practice 1. Write 70,304 in expanded form and words. Include every zero place in your working.

Show the complete place-value solution

70,304

$$70,304=7\times10,000+0\times1,000+3\times100+0\times10+4$$

$$70,304=70,000+300+4$$

$$\text{seventy thousand three hundred and four}$$

Practice 2. Order 46,528, 46,582, 40,006 and 100,000 from least to greatest.

Show the comparison solution

Compare highest places

$$40,006<46,528<46,582<100,000$$

$$\text{The thousands place separates 40,006 from the 46,xxx numbers; tens decide 46,528 and 46,582; 100,000 has six digits.}$$

Practice 3. Round 46,582 to the nearest 10, nearest 100 and nearest 1,000.

Show all three rounding solutions

Choose the requested place

$$46,582\rightarrow46,580\text{ (nearest 10)}$$

$$46,582\rightarrow46,600\text{ (nearest 100)}$$

$$46,582\approx47,000\text{ (nearest 1,000)}$$

Watch out — easily mixed up

Quick recap

🎯 Mastery check

Answer all 6 — your progress is saved on this device.

1. What is the value of the 6 in 46,582?

   6,00060060

2. Which words name 40,006?

   four thousand and sixforty thousand and sixforty thousand and sixty

3. Which order is least to greatest?

   46,582, 46,528, 40,00640,006, 46,528, 46,58246,528, 40,006, 46,582

4. What comes next: 12,000, 13,000, 14,000, …?

   14,10015,00016,000

5. 46,582 rounded to the nearest 100 is…

   46,50046,58046,600

6. Which statement shows a rounded value correctly?

   46,582 ≈ 47,00046,582 = 47,00046,582 ≈ 46,580 exactly

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