Basic Mathematics

Expanded Notation

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Expanded Notation
Expanded Notation - In expanded notation a number is written as the sum of the values of each of its digits.
Sometimes the place values are written as numbers, sometimes as powers of ten, and sometimes as words.
145 = 100 + 40 + 5
145 = (1 × 100) + (4 × 10) + (5 × 1)
145 = (1 × 102) + (4 × 101) + (5 × 100)
145 = 1 hundred + 4 tens + 5 ones
145 = one hundred forty-five
Expanded Notation
This place value chart shows some place values that are equal to and greater than one.
Expanded Notation
This place value chart shows some place values that are equal to and less than one.
Expanded Notation
Shown below are forms of expanded notation for a decimal numeral.
4.75 = 4 + 0.7 + 0.05
4.75 = (4 ×1) + (7 × 0.1) + (5 × 0.01)
4.75 = (4 × 100) + (7 × 10−1) + (5 × 10−2)
4.75 = 4 ones + 7 tenths + 5 hundredths
The decimal point in a number is read in words as "and."
4.75 = four and seventy-five hundredths
Expanded Notation
Click on the numeral equivalent to this word name.
Three hundred seventy-two
30,072
 3,072
    372
 3,702
None of these
Question 1 of 8
30,072 is read "thirty thousand seventy-two." Try again.
3,072 is read "three thousand seventy-two." Try again.
300 + 72 = 372
3,702 is read "three thousand seven hundred two." Try again.
One of these is correct. Try again.
Three hundred seventy-two = 3 hundreds + 7 tens + 2 ones
Expanded Notation
Click on the word name equivalent to this numeral.
20,070
Twenty thousand,seven hundred
Twenty thousand, seventy
Two thousand, seventy
Twenty seventy
None of these
Question 2 of 8
"Twenty thousand, seven hundred" is equivalent to 20,700. Try again.
The digits to the left of the comma are read "twenty thousand" and to the right of the comma "seventy."
"Two thousand, seventy" is equivalent to 2,070. Try again.
The 2 in 20,070 is read as twenty thousand, not just twenty. Try again.
One of these is correct. Try again.
20,070 = 2 ten thousands + 7 tens
Expanded Notation
Click on the numeral equivalent to this expanded notation.
8 ones + 5 tens + 7 hundreds + 3 thousands
  8,573
30,758
  3,758
      23
None of these
Question 3 of 8
8,573 = 8 thousands + 5 hundreds + 7 tens + 8 ones.
Try again.
The value of 3 thousands is 3,000, not 30,000. Try again.
8 + 50 + 700 + 3000 = 3,758
23 is the sum of 8 + 5 + 7 + 3. The value of 3 thousands is 3,000. Try again.
One of these is correct. Try again.
3 thousands + 7 hundreds + 5 tens + 8 ones = 3,000 + 700 +50 +8.
Expanded Notation
Click on the numeral equivalent to this expanded notation.
(5 × 10) + (7 × 0.1) + (8 × 0.01)
50.708
  5.078
50.78
  5.78
None of these
Question 4 of 8
The 8 belongs in the hundredths place, not the thousandths place. Try again.
The whole number part is 5 × 10 or 50, not 5. Try again.
50 + 0.7 + 0.08 = 50.78
The whole number part is 5 × 10 or 50, not 5. Try again.
One of these is correct. Try again.
(5 × 10) + (7 × 0.1) + (8 × 0.01) = 50 + 0.7 + 0.08
Expanded Notation
Click on the expanded notation equivalent to this numeral.
6,023
(6 × 1000) + (2 × 10) + (3 × 1)
(6 × 100) + (2 × 10) + (3 × 1)
(6 × 10,000) + (2 × 10) + (3 × 1)
(6 × 1000) + (2 × 100) + (3 × 1)
None of these
Question 5 of 8
6,023 = 6000 + 20 + 3
= (6 × 1000) + (2 × 10) + (3 × 1)
(6 × 100) + (2 × 10) + (3 × 1)= 623. Try again.
(6 × 10,000) + (2 × 10) + (3 × 1)= 60,023. Try again.
(6 × 1000) + (2 × 100) + (3 × 1)= 6,203. Try again.
One of these is correct. Try again.
6,023 = 6,000 + 20 +3
Expanded Notation
Click on the word name equivalent to this numeral.
8.07
Eighty-seven
Eight and seven tenths
Eight and seven thousandths
Eight hundred seven
None of these
Question 6 of 8
"Eighty-seven" is equivalent to 87. Try again.
"Eight and seven tenths" is equivalent to 8.7. Try again.
"Eight and seven thousandths" is equivalent to 8.007. Try again.
"Eight hundred seven" is equivalent to 807. Try again.
The word name is "eight and seven hundredths."
This numeral contains a whole number and a decimal.
Expanded Notation
Click on the numeral equivalent to this expanded notation.
(7 × 103) + (5 × 102) + (3 × 101) + (0 × 100)
     753
75,310
75,301
  7,530
None of these
Question 7 of 8
753 = (7 × 102) + (5 × 101) + (3 × 100). Try again.
75,310 = (7 × 104) + (5 × 103) + (3 × 102) + (1 × 101) + (0 × 100). Try again.
75,301 = (7 × 104) + (5 × 103) + (3 × 102) + (0 × 101) + (1 × 100). Try again.
7000 + 500 + 30 + 0 = 7,530
One of these is correct. Try again.
(7 × 103) + (5 × 102) + (3 × 101) + (0 × 100)
= 7,000 + 500 + 30 +0
Expanded Notation
Click on the numeral equivalent to this expanded notation.
(4 × 100) + (3 × 10−2)
  0.43
43
  4.03
40.3
None of these
Question 8 of 8
0.43 is equivalent
to (4 × 10−1) + (3 × 10−2). Try again.
43 is equivalent
to (4 × 101) + (3 × 100). Try again.
4 is in the ones place. 3 is in the hundredths place.
40.3 is equivalent to
(4 × 101) + (3 × 10−1). Try again.
One of these is correct. Try again.
(4 × 100) + (3 × 10−2)
= 4 ones + 3 hundredths
Expanded Notation