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Percentages are a way to express numbers as a fraction of 100. The term 'percent' comes from the Latin 'per centum', which means 'by the hundred'. We frequently use percentages to compare proportions, express probability, or indicate changes in quantities. For instance, if you score 90% on a test, this means you got 90 out of every 100 possible points.

Understanding the relationship between decimals and percentages is crucial in mathematics and everyday life, as it allows you to interpret and communicate numerical information effectively. When you see a discount marked as 20%, it means that the original price is reduced by 20 out of every 100 units of currency, be it dollars, euros, or another currency.

Decimal numbers are a way of representing fractions and real numbers without using fractions. A decimal number is a number that has a whole number part and a fractional part separated by a decimal point (for example, 3.14). The digits to the right of the decimal point show a value smaller than one, with each position representing a negative power of 10.

Understanding decimals is crucial because it makes it easier to perform calculations than using fractions. Many everyday measurements, such as currency and length, are commonly expressed using decimal numbers. In our exercise, the decimals work as a more convenient way to represent percentages, since they can be directly converted to one another.

Multiplication by 100 is a basic arithmetic operation that involves increasing a number a hundredfold. When you multiply a decimal number by 100, you are essentially shifting the decimal point two places to the right, or adding two zeros to the end of the number if there are no digits after the decimal. This is because 100 has two zeros, which is why we move the point two places.

For example, multiplying 1.5 by 100 gives us 150. This method is particularly useful when converting decimal numbers to percentages since percentages are based per hundred. So, when you come across a decimal like 0.085 and need to find out what percentage it represents, multiplying by 100 will easily convert it to 8.5%.