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3 years ago

Place value with tenths

2 answers:

5 0

6,702 = 6 thousands and 7 hundreds and 0 tens and 2 ones
= 6 × 1000 + 7 × 100 + 0 × 10 + 2 × 1
= 6000 + 700 + 2.

Above, we have written the number 6,702 in expanded form, or as a SUM of its different parts according to place value.

The digit 6 in the number 6,702 actually has the value 6,000 and the digit 7 actually signifies the value 700. This is why our number system is also called a place value system, because the value of a digit (like 6 or 7 in our example) depends on its placement within the number. In other words, the digit 6 in 6702 does not mean six but six thousand, because the six is placed in the thousands' place. The place of a digit determines its value.

The comma between thousands and hundreds is added as a separator for easier reading. In some countries an empty space is used instead: 6,702 is written as 6 702.

Talja [164]3 years ago

3 0

Tenths isn't the the the number on the right of the decimal. Example tenth=1 so 0.1

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Finger [1]

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G8. -2+√7

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Step-by-step explanation:

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$\dfrac{3}{2 +\sqrt{7}}=\dfrac{3}{2+\sqrt{7}}\cdot\dfrac{2-\sqrt{7}}{2-\sqrt{7}}=\dfrac{6-3\sqrt{7}}{2^2-(\sqrt{7})^2}\\\\=\dfrac{6-3\sqrt{7}}{-3}=\sqrt{7}-2$

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$\dfrac{2-\sqrt{3}}{3-\sqrt{2}}=\dfrac{2-\sqrt{3}}{3-\sqrt{2}}\cdot\dfrac{3+\sqrt{2}}{3+\sqrt{2}}=\dfrac{(2-\sqrt{3})(3+\sqrt{2})}{9-2}\\\\=\dfrac{6+2\sqrt{2}-3\sqrt{3}-\sqrt{6}}{7}$

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<em>Comment on the problems</em>

In most cases, these expressions are the simplest possible (take the least amount of ink to draw, and take the fewest math operations to evaluate). What seems to be intended is that the denominator be made a rational number. This is done by multiplying the given fraction by a fraction equal to 1 that has the same denominator but with the sign of the radical reversed (unless, as in the first case, the radical is by itself).

The purpose of doing this is to take advantage of the fact that (a-b)(a+b) = a²-b², so if "a" or "b" is a square root, that root will not be seen in the product. In problem G9, we see this can make the numerator quite messy--not exactly a simpler form--but all the irrational numbers are in the numerator.

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