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1. Base Ten Number System The common number system we use. Our number system is based on the number 10 because we have ten fingers with which to group. Each group represents ten of the previous group, so we can write numbers efficiently.
By extending the place value system to include places that represent fractions with 10 or powers of 10 in the denominator, we can easily represent very large and very small quantities.
2. Benchmark A reference number that can be used to estimate the size of other numbers. For work with fractions, 0, , and 1 are good benchmarks. We often estimate fractions or decimals with benchmarks because it is easier to do arithmetic with them, and estimates often give enough accuracy for the situation.
For example, many fractions and decimalssuch as 37/50 , 5/8, 0.43, and 0.55can be thought of as being close to .
You might say 5/8 is between and 1 but closer to , so you can estimate 5/8 to be about .
We also use benchmarks to help compare fractions and decimals.
For example, we could say that 5/8 is greater than 0.43 because 5/8 is greater than and 0.43 is less than .
3. Decimal A special form of a fraction. Decimals, or
decimal fractions, are based on the base ten
place-value system. To write numbers as decimals,
we use only 10 and powers of 10 as denominators.
Writing fractions in this way saves us from writing
the denominators because they are understood.
When we write 375 as a decimal (0.375) the
denominator of 1,000 is understood. The digits to the
left of the decimal point show whole units. The digits
to the right of the decimal point show a portion of a
4. Denominator The number written below the line in
a fraction. In the fraction 3/4, 4 is the denominator.
In the part-whole interpretation of fractions, the denominator shows the number of equal-size parts into which the whole has been split.
5. Equivalent Fractions Fractions that are equal in value, but may have different numerators and denominators. For example, 2/3 and 14/21 are equivalent fractions. The shaded part of this rectangle represents both 2/3 and 14/21.