The scale of a map is 1:25000.Find the actual length of a road,in cm,which is measured 7.8 cm on the map.Express the answer in standard form.
25,000 x 7.8=195,000
To find the actual length of a road given the scale of a map and the measured length on the map, follow these steps:
1. Determine the scale of the map. In this case, the scale is given as 1:25000. This means that 1 unit on the map represents 25000 units in actual distance.
2. Calculate the actual length of the road. Since the measured length on the map is 7.8 cm, we need to convert it to actual distance. To do this, divide the measured length on the map by the scale.
Actual length of the road = measured length on the map / scale
= 7.8 cm / 25000
3. Simplify the fraction in the expression. To express the answer in standard form, divide both the numerator and denominator by the greatest common divisor (GCD) of the two numbers.
GCD(7.8, 25000) = 0.2
Actual length of the road = (7.8 cm / 0.2) / (25000 / 0.2)
= 39 cm / 5000
= 0.0078 cm
4. Express the result in standard form. To write this number in standard form, move the decimal point to after the first significant digit, and adjust the exponent accordingly. In this case, the decimal point should be moved 3 places to the right, resulting in:
Actual length of the road = 7.8 x 10^-3 cm
Therefore, the actual length of the road is 7.8 x 10^-3 cm.