This is a complete lesson v instruction and exercises about decimals with 3 decimal digits: composing them as fractions, ar value & expanded form, and also decimals ~ above a number line. That is supposed for 5th grade.

You are watching: Write six thousandths in standard form

In the video clip below, I describe decimals with three decimal digits—or thousandths—using fractions and a number line. Climate I present examples that converting fountain to decimals and also vice versa.

 This square illustrates one whole. It is split into a hundred parts or hundredths. The optimal left square is separated into ten new parts. Those space thousandths.The 6 shaded parts represent 61000 , or 0.006 (six thousandths).

The 3rd decimal number from the decimal point is the thousandths digit.For example, 0.008 is eight thousandths.

Read the whole set of three decimal digits together a number, and also say “thousandths.”

 0.391 is check out “391 thousandths.” as a fraction, that is 3911000 .
 0.047 is review “47 thousandths.” together a fraction, it is 471000 .
From the location value chart, we deserve to see that the number0.825 has 8 tenths, 2 hundredths, and 5 thousandths.

Writing 0.825 as a sum of those “parts” is called writing the in expanded form.

 O t h th 0 . 8 2 5

 0.825 = 8 × 110 + 2 × 1100 + 5 × 11000

While 0.825 is the amount of 8/10, 2/100, and also 5/1000, the is additionally 825/1000 (825 thousandths). How deserve to that be?

Because 8/10 is equal to 800/1000 and also 2/100 is same to 20/1000. So, when you add 8/10, 2/100, and 5/1000, you will get 825/1000.

1. Compose the numbers in their increased form. Write them likewise as fractions. The first one is done for you.

 a. O t h th 0 . 9 0 6
=9061000

 = 9 × 110 + 0 × 1100 + 6 × 11000

b.

 O t h th 0 . 2 4 4
=

 =× 110 + × 1100 + × 11000

c.

 O t h th 0 . 6 5 5
=

 =× 110 +

d.

 O t h th 0 . 1 8
=

 =

e.

 O t h th 0 . 8 0 2
=

 =× 110 +

f.

 O t h th 0 . 7 1 1
=

 =

2. This numbers have likewise hundreds, tens, and also ones. Write the numbers in the broadened form. Follow the example.

 a. T O t h th 6 3 . 9 2 6
= 6 × 10 + 3 × 1 + 9 × 110 + 2 × 1100+ 6 ×11000b.
 T O t h th 2 4 . 7 8 8
= × 10 + × 1 + × 110 + × 1100+ ×11000c.
 T O t h th 4 . 9 0 2
= × 1 +d.
 T O t h th 7 4 . 7 2
= e.
 H T O t h th 1 5 1 . 9
=× 100 + f.
 H T O t h th 7 6 5 . 2 4 4
=× 100 + 3.Write the decimal in the location value charts, and as fractions.

 a. 7 thousandths O t h th .

=

b. 8 tenths and 2 thousandths

 O t h th .

=

c. 3 and also 371 thousandths

4. Compose in increased form.

a. 0.95 =

b. 1.405 =

c. 244.781 =

d. 65.05 =

e. 20.214 =

=

d. 39 thousandths

 O t h th .
=

e. 1 and also 41 hundredths

 O t h th .
=

f. 7 and also 4 thousandths

 O t h th .
=
 This number line has actually tick marks in ~ every hundredth. Because that thousandths, we would should divide each together interval right into ten new intervals. Imagine that in between each two tick clues there room nine small lines. Those would stand for thousandths.The number 0.052, 0.145, 0.228, and 0.304 are marked on the number line. Have the right to you uncover them? Reminder: You deserve to “tag” zeros ~ above the end of a decimal number,and its worth will no change: O t h th 0 . 7 0 . 7 0 0 . 7 0 0
0.7
 = 0.70 = 0.700 Seven tenths = 70 hundredths = 700 thousandths 710 = 70100 = 7001000

5. To fill in through the kind of components you get.

When you division one totality into ten equal parts,you get _________________________________.

When you divide one tenth right into ten equal parts,you acquire _________________________________.

When you division one hundredth into ten equal parts,you acquire ______________________________.

6.Write the decimals indicated by the arrows.

a. ____________ b. ____________ c. ____________ d. ____________ e. ____________

7. Mark these decimal on the number line: 0.187, 0.205, 0.252, 0.301, and 0.314.

8.Write the fractions together decimals.

 a. 31000 =
b.
 121000 =
c.
 3191000 =
d.
 501000 =
e. 4
 341000 =
f. 2
 41000 =
g. 3
 3100 =
h. 1
 80100 =
i. 17
 31000 =
j.
 6491000 =
k. 9
 1100 =
l. 50
 6191000 =

9.Write as fractions or combined numbers.

 a. 0.048 b. 3.902 c. 3.005 d. 6.7 e. 10.06 f. 12.060 g. 7.90 h. 0.429 i. 505.5 j. 4.789 k. 0.091 l. 5.42

10. What number is developed from the "parts"? offer your answer as a decimal.

 a. 31000 + 210 + 7100 =
b.
 810 + 1 + 9100 =
c.
 210 + 7 + 31000 =
d.
 510 + 90 + 2100 = 81000 =
e.
 110 + 7 + 81000 + 10 =
f.
 200 + 81000 + 5 =
11. Ten tenths provides one whole. We deserve to write that together a multiplication: 10 × 0.1 = 1. (Note: the word “makes” synchronizes to the equal sign, but there is no word to correspond to the multiplication sign; it is implied.) to fill in the sentence below, and write a multiplication sentence to enhance each one. Hint: The photo of the huge square in the an initial page of this lesson have the right to help.

 a. ________ thousandths makes a hundredth. _______ × _______ = _______ b. ________ hundredths makes a tenth. _______ × _______ = _______ c. ________ thousandths renders a tenth. _______ × _______ = _______ d. ________ hundredths provides one whole. _______ × _______ = _______

12.Use the place value chart to assist you, and write the decimal that is....

 a. O t h th 0 . 2 8 5

one tenth more than 0.285 _________

one hundredth an ext than 0.285 _________

one thousandth more than 0.285 _________

b.
 O t h th .

one tenth an ext than 0.016 _________

one hundredth much more than 0.016 _________

one thousandth much more than 0.016 _________

c.
 O t h th .

one tenth an ext than 1.07 _________

one hundredth an ext than 1.07 _________

one thousandth much more than 1.07 _________

d.
 O t h th .

one tenth an ext than 0.9 _________

one hundredth much more than 0.9 _________

one thousandth much more than 0.9 _________

e.
 O t h th .

five tenths more than 2.316_________

six hundredths more than 2.316 _________

two thousandths more than 2.316 _________

f.
 T O t h th .

ten much more than 1.08 _________

one hundredth an ext than 1.08 _________

nine thousandths an ext than 1.08 _________