TEACHER ABI PSHS NCE · QUANTITATIVE ABILITY

Whole Numbers and Place Value

Read big numbers correctly, compare them quickly, round wisely, and use number sense to catch impossible answers.

Grade 6–7 friendly Worked examples Regular practice Quick Fire + Mastery

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Whole Numbers and Place Value

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Every digit has a job

Look at this number:

4,582,731

The digit 5 does not mean just “five.” Because it is in the hundred-thousands place, its value is 500,000.

Place = where the digit sits.
Value = what the digit is worth in that place.

So in 4,582,731:

8
ten-thousands place
80,000

2
thousands place
2,000

7
hundreds place
700

3
tens place
30

DO IT FAST

Use LOOK → COMPARE → CHECK

1. LOOK: Start from the leftmost digit.
2. COMPARE: The first place where the digits are different decides which number is greater.
3. CHECK: If rounding or estimating, ask: “Is my answer close to the original number?”

Which is greater: 684,921 or 684,291?

The hundred-thousands, ten-thousands, and thousands digits are the same. Compare the hundreds: 9 > 2.

684,921 is greater. You do not need to compare the remaining digits.

WORKED EXAMPLES

Five patterns you should recognize

1. Place value

7,316,405

What is the value of the digit 3?

300,000. The 3 is in the hundred-thousands place.

2. Compare big numbers

Which is greater: 509,842 or 509,824?

Compare from the left. The first difference is in the tens place: 4 tens vs 2 tens.

509,842 is greater.

3. Round to the nearest thousand

Round 46,582 to the nearest thousand.

Look at the hundreds digit: 5. Five or more means round up.

47,000

4. Estimate before solving

About how much is 3,982 + 6,117?

Round to friendly numbers: 4,000 + 6,000.

About 10,000.

5. Catch an impossible answer

A student says 8,052 − 3,978 = 12,030.

Impossible. Subtracting a positive number from 8,052 cannot give an answer larger than 8,052.

TRY WITH ME

Compare without doing extra work

Which is greater?

672,418   or   672,481

1. Are the hundred-thousands digits the same? Yes.
2. Are the ten-thousands digits the same? Yes.
3. Are the thousands digits the same? Yes.
4. Now compare the hundreds digits: 4 and 4. Still tied.
5. Compare the tens digits: 1 and 8.

672,481 is greater. The first different place is the tens place, and 8 tens is greater than 1 ten.

COMMON TRAPS

Watch out for these

Reading only the last digits.
Compare numbers from the left.

Mixing up place and value.
A digit 6 in the thousands place has value 6,000.

Rounding the wrong digit.
Look one place to the right of the place you are rounding.

Skipping estimation.
A quick estimate can expose a bad answer immediately.

REGULAR PRACTICE

Build the skill

Work carefully. These questions mix place value, comparison, rounding, and estimation.

QUICK FIRE

Can you spot it fast?

Five short questions. Try to answer each without writing a full solution.

Question 1 of 5

FRESH MASTERY CHECK

Can you do it without hints?

Score 5/5 to verify this competency. If you miss one, review the explanation and try the fresh set.

NEED HELP?

Not sure why a number question keeps catching you?

Send Teacher Abi your result. I can help you figure out which part of the skill needs more practice.

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PSHS NCE REVIEW PATH

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Next competency: Factors, Multiples, and Divisibility

Whole NumbersPlace ValueRoundingEstimation

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