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one tenth, so now, in the same way, if he takes ten thousandths, he will have one hundredth.
Write ten thousandths for him as a decimal. .010. Explain that as in common fractions we reduce to lowest terms to simplify, so in decimal fractions, when we get ten parts of one name, we drop that name, and call it one of the next higher order.
So, to write ten thousandths as a decimal simplified, we leave out the last 0, and write it .01. Read, one hundredth.
NOTE. You may say that the 0, when at the right of a decimal fraction, may be omitted, because it has no value. It simply shows a decimal not in its lowest terms. This is true only when it is not followed by another figure.
After drill similar to that outlined here, he is ready to be given the "decimal places," as they are called, and their names.
The first place is tenths.
The second place is hundredths.
The seventh place is ten-millionths, etc.
.000000002 two billionths.
Let the child write other numbers for each place and read them to you.
Explain in a nice way how easy it is in this man
ner to write fractions that have ten, or some multiple of ten, for a denominator. The figures of the numerator put in the right place and the decimal point, do all.
The same law holds good here that the child found true in writing integers :
Ten units of any order make one unit of the next higher order.
The place of the right-hand figure in a decimal fraction shows the name of the denominator, as,
The name of the figure to the right in the third place is thousandths, so the denominator is thousandths.
Have the child name the denominators of many decimal fractions, as,
NOTE.-Go over every step taken so far, until you are sure the pupil understands all clearly. If he does, the remainder of the work will be so much easier for him. Be sure that he gets each step.
Go slow and be thorough.
WHOLE NUMBERS WITH DECIMAL FRACTIONS.
The child will have no trouble reading whole numbers with decimal fractions attached to them.
You need only tell him to read the whole number as if there were no decimal fraction, say “and,” and read the decimal fraction as if there were no whole number attached to it. The "and" connects them.
Some teachers have the children read such numbers in two ways:
(a) one ter, four units, and three tenths.
(b) fourteen, and three tenths.
USE OF WORD "AND."
You often hear people read a number like 347 in this way:
"Three hundred and forty-seven."
Why not read it—
"Three hundred forty-seven," which is the correct
Omit the "and" in every whole number or mere decimal fraction.
six hundred ninety-six.
seven thousand two hundred forty.
two hundred six thousandths.
When there is a whole number with a decimal fraction, read "and" at the decimal point.
thirty-two and four tenths.
624.112 six hundred twenty-four and one hundred twelve thousandths.
Call the decimal point "and," in reading numbers having decimal fractions.
With this idea firmly fixed and carried out in practice, the child will know just where the decimal point comes, when a number is read to him.
He is now ready to write numbers with decimal fractions, as well as to read them.
Any part of a number may be read by giving the part read the name of its last figure, as, 4.35 is fortythree tenths and five hundredths.
26.143 is two thousand six hundred fourteen hundredths and three thousandths.
Read the following as indicated above:
Teach that any number may be read by giving the name of the right-hand figure to the whole number, as,
135 is one hundred thirty-five units.
4.27 is four hundred twenty-seven hundredths.
A good way to teach this is given here:
36 3 tens + 6 units = 36 units.
2.52 units + 5 tenths = 25 tenths.
.0252 hundredths + 5
thousandths = 25
= 25 thou
3.145 3 units + 1 tenth + 4 hundredths + 5 thou
sandths 3145 thousandths.
Try many examples like these, using simple ones until the pupil sees what is wanted.
Do this now and the pupil will have less trouble in understanding division of decimals.
Be sure the work is thorough.
Reduction of Decimal Fractions to Common
This work may be made a pleasure to the pupil. The only feature of it he has not had previously is the connection between the decimal, as such, and its final form as a common fraction in its lowest terms. Call his attention to this.
Have the child take the decimal fraction and after reading it aloud, write it as a common fraction. This done, let him reduce the new form to lowest terms.
He may talk it this way:
The decimal fraction, five tenths, equals the common fraction, five tenths. This reduced to lowest terms is one half. Give many like the following:
Follow the above work with this:
Reduce 42.5 to a mixed number.
Have the pupil pay no attention to the whole number. Taking the decimal .5, he treats it as in the previous exercise. It equals. Now add it to the whole number. The result is 421.