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tekilochka [14]
3 years ago
11

What decimal is shown by the shaded area in the model​

Mathematics
1 answer:
Arisa [49]3 years ago
8 0

Answer:

.001

OR

1/100

OR

one hundredth

(remember the "th")

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The digit 5 appears twice in the number 255,120. How does the total value of the 5 on the right compare to the total value of th
maksim [4K]

Answer:

The value of the first "5" in the number 255,\!120 is ten times that of the second "5\!" in this number.

Step-by-step explanation:

What gives the number "255,\!120" its value? Of course, each of its six digits has contributed. However, their significance are not exactly the same. For example, changing the first \verb!5! to \verb!6! would give 2\mathbf{6}5,\!120 and increase the value of this number by 10,\!000. On the other hand, changing the second \verb!5!\! to \verb!6!\! would give 25\mathbf{6},\!120, which is an increase of only 1,\!000 compared to the original number.

The order of these two digits matter because the number "255,\!120" is written using positional notation. In this notation, the position of each digits gives the digit a unique weight. For example, in 255,\!120\!:

\begin{array}{|r||c|c|c|c|c|c|}\cline{1-7}\verb!Digit!& \verb!2! & \verb!5! & \verb!5! & \verb!1! & \verb!2! & \verb!0!\\\cline{1-7}\textsf{Index} & 5 & 4 & 3 & 2 & 1& 0 \\ \cline{1-7} \textsf{Weight} & 10^{5} & 10^{4} & 10^{3} & 10^{2} & 10^{1} & 10^{0}\\\cline{1-7}\end{array}.

(Note that the index starts at 0 from the right-hand side.)

Using these weights, the value 255,\!120 can be written as the sum:

\begin{aligned}& 255,\!120\\ &= 2 \times 10^{5} + 5 \times 10^{4} + 5 \times 10^{3} + 1 \times 10^{2} + 2 \times 10^{1} + 0 \times 10^{0} \\&=200,\!000 + 50,\!000 + 5,\!000 + 100 + 20 + 0 \end{aligned}.

As seen in this sum, the first "5" contributed 50,\!000 to the total value, while the second "5\!" contributed only 5,\!000.

Hence: The value of the first "5" in the number 255,\!120 is ten times that of the second "5\!" in this number.  

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