Numbers to 1,000,000
4A · Chapter 1 · Lesson 2 · MATH-4A-C01-L02
Learning goal. Build and rename six- and seven-digit quantities, including ten hundred-thousands as one million.
Before you begin
Recall: Grade 3: four-digit place value, regrouping, comparison and rounding; Numbers to 100,000. Try these three warm-up problems. If they are difficult, revisit the prerequisite lesson before advancing.
How many complete groups of 10 can be made from 14,025 objects, and how many remain?
Show answer & reasoning
14,025 = 1402 × 10 + 5.
From 23,563 add 6 groups of 10.
Show answer & reasoning
6 groups of 10 are 60; then add to the starting value.
In 90,069, what is the value of the digit in the ten-thousands place?
Show answer & reasoning
The digit 9 represents 9 groups of 10,000, or 90,000.
Key vocabulary
- place value
- value determined by a digit position
- expanded form
- sum of each nonzero place value
- benchmark
- nearby convenient multiple
- midpoint
- number exactly halfway between two bounds
Understand the concept
A million is ten groups of one hundred-thousand. To read 506,014, name the thousands group and then the ones group: five hundred six thousand fourteen. A placeholder zero tells you a place has no units, but it still matters to the written numeral. Exchanging ten lower units for one higher unit preserves the quantity.
Model it: million-place chart and ten-to-one exchanges. Explain what every part of the model represents, then write a matching equation.
Fully worked examples
Read the problem first and predict the answer. Then study how each quantity is represented and calculated.
Worked example 1
In 742,541, what is the value of the digit in the hundred-thousands place?
The digit 7 represents 7 groups of 100,000, or 700,000.
Check your understanding 1
In 973,910, what is the value of the digit in the hundred-thousands place?
Show answer & reasoning
The digit 9 represents 9 groups of 100,000, or 900,000.
Worked example 2
Write 797,313 as a number of whole thousands and remaining ones.
797 × 1,000 + 313 = 797,313. This grouping preserves the original value.
Check your understanding 2
Write 424,878 as a number of whole thousands and remaining ones.
Show answer & reasoning
424 × 1,000 + 878 = 424,878. This grouping preserves the original value.
Worked example 3
Find 754,240 − 753,240 and explain the place-value change.
Only the increment changes: 754,240 − 753,240 = 1,000.
Check your understanding 3
Find 437,660 − 337,660 and explain the place-value change.
Show answer & reasoning
Only the increment changes: 437,660 − 337,660 = 100,000.
Guided practice
In 958,037, what is the value of the digit in the hundred-thousands place?
Show answer & reasoning
The digit 9 represents 9 groups of 100,000, or 900,000.
Write 125,094 as a number of whole thousands and remaining ones.
Show answer & reasoning
125 × 1,000 + 94 = 125,094. This grouping preserves the original value.
Find 162,063 − 161,063 and explain the place-value change.
Show answer & reasoning
Only the increment changes: 162,063 − 161,063 = 1,000.
Multiply 5,513 by 100.
Show answer & reasoning
Scaling each place value by 100 gives 551,300.
How many complete groups of 10 can be made from 622,225 objects, and how many remain?
Show answer & reasoning
622,225 = 62222 × 10 + 5.
Independent practice
Write 493,906 as a number of whole thousands and remaining ones.
Show answer & reasoning
493 × 1,000 + 906 = 493,906. This grouping preserves the original value.
Find 704,788 − 604,788 and explain the place-value change.
Show answer & reasoning
Only the increment changes: 704,788 − 604,788 = 100,000.
Multiply 3,396 by 100.
Show answer & reasoning
Scaling each place value by 100 gives 339,600.
How many complete groups of 10 can be made from 521,793 objects, and how many remain?
Show answer & reasoning
521,793 = 52179 × 10 + 3.
From 258,277 add 4 groups of 10,000.
Show answer & reasoning
4 groups of 10,000 are 40,000; then add to the starting value.
In 976,190, what is the value of the digit in the hundred-thousands place?
Show answer & reasoning
The digit 9 represents 9 groups of 100,000, or 900,000.
Write 578,645 as a number of whole thousands and remaining ones.
Show answer & reasoning
578 × 1,000 + 645 = 578,645. This grouping preserves the original value.
Find 295,445 − 294,445 and explain the place-value change.
Show answer & reasoning
Only the increment changes: 295,445 − 294,445 = 1,000.
Challenge and transfer
Explain the relationships and justify your method. Multiple correct approaches may be accepted if the reasoning is valid.
A student removes the zeros from 204,006, saying zeros never affect place value. Explain why this is incorrect.
Show answer & reasoning
The zeros preserve each digit position: the number contains 2 hundred-thousands, 4 thousands, and 6 ones. Removing them changes the value.
In 882,845, what is the value of the digit in the hundred-thousands place?
Show answer & reasoning
The digit 8 represents 8 groups of 100,000, or 800,000.
Exit check
Multiply 1,000 by 1000.
Show answer & reasoning
Scaling each place value by 1000 gives 1,000,000.
How many complete groups of 100 can be made from 909,738 objects, and how many remain?
Show answer & reasoning
909,738 = 9097 × 100 + 38.
From 396,308 add 5 groups of 10,000.
Show answer & reasoning
5 groups of 10,000 are 50,000; then add to the starting value.