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Alex777 [14]
1 year ago
7

A map shows the town where Niko lives. The actual distance from Niko's house to his school is 3 miles, and measures one-half inc

h on the map. The actual distance from Niko's school to the library is 4 miles. How long is this distance on the map?
Mathematics
2 answers:
Temka [501]1 year ago
6 0

<u>Answer:</u>

The distance is 2 inches in map

<u>Explanation:</u>

Given, the actual distance between Niko’s house and his school is 3 miles

In map, the distance is one half inch (1.5 inch)

Therefore, 1.5 inch (in map) = 3 miles (actual)

If the actual distance is 4 miles

Then, distance in maps is \frac{4 \times 1.5}{3} =2 inches

Hence, the distance is 2 inches in map

katrin2010 [14]1 year ago
3 0

Answer:

<u>The distance of the library in the map is 0.67 inches (Rounding to two decimal places)</u>

Step-by-step explanation:

1. Let's review all the information given for solving this question:

Scale factor for the map of the town = 0.5 inches: 3 miles

Distance from Niko's house to his school = 3 miles

Distance from Niko's school to the library = 4 miles

2. Let's find the distance of the library in the map

Distance of the library in the map = Distance of the library * Scale factor

Distance of the library in the map = 4 miles * 0.5 inches:3 miles

Distance of the library in the map = (2 miles * inches)/3 miles

Distance of the library in the map = 2 inches/3 (Miles are cancelled in the numerator and in the denominator)

<u>Distance of the library in the map = 0.67 inches (Rounding to two decimal places)</u>

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<em><u>The three equivalent numerical expressions are:</u></em>

(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})

(0.0004) . (0.005)= (\frac{1}{2500}).(\frac{1}{200})

(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})

<em><u>Solution:</u></em>

We have to write three numerical expressions that are equivalent to (0.0004) . (0.005)

<em><u>Given expression is:</u></em>

(0.0004) . (0.005)

<em><u>First numerical expression:</u></em>

We know that 0.0004 can be written in fraction as:

0.0004 = \frac{0.0004 \times 10000}{10000} = \frac{4}{10000}

Similarly,

0.005 = \frac{0.005 \times 1000}{1000} = \frac{5}{1000}

Therefore,

(0.0004) . (0.005) = (\frac{4}{10000}).(\frac{5}{1000})

<em><u>Second numerical expression:</u></em>

The first numerical expression can be simplified to get second numerical expression

(\frac{4}{10000}).(\frac{5}{1000}) = (\frac{1}{2500}).(\frac{1}{200})

<em><u>Third numerical expression:</u></em>

The given expression can be expressed in scientific notation:

<em><u>Steps for converting to scientific notation:</u></em>

Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.

Count how many places you moved the decimal point. This number is b.

If you moved the decimal to the left b is positive.

If you moved the decimal to the right b is negative.

If you did not need to move the decimal b = 0.

Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b."

Remove trailing 0's only if they were originally to the left of the decimal point.

0.0004 = 4 \times 10^{-4}\\\\0.005 = 5 \times 10^{-3}

Therefore, third equivalent numerical expression is:

(0.0004) . (0.005) = (4 \times 10^{-4}).(5 \times 10^{-3})

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Step-by-step explanation:

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Your question has been heard loud and clear.

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