Multiply and divide decimals by powers of ten

Learning Objectives Identify powers of ten (e.g., 10, 100, 0.1, 0.01). Explain the effect of multiplying a decimal by a power of ten. Explain the effect of dividing a decimal by a power of ten. Multiply any decimal by a positive power of ten (10, 100, 1000...). Divide any decimal by a positive power of ten (10, 100, 1000...). Solve real-world problems involving multiplying and dividing decimals by powers of ten. Ever wonder how scientists quickly convert measurements like meters to kilometers or grams to milligrams? 📏 It's all about powers of ten! In this lesson, you'll discover simple tricks for multiplying and dividing decimals by powers of ten, like 10, 100, or 0.1. This skill will make calculations much faster and help you understand how numbers relate to dif...

TermDefinitionExample DecimalA number that includes a whole number part and a fractional part, separated by a decimal point.3.14, 0.5, 12.0 Power of TenA number that can be expressed as 10 raised to an integer exponent (e.g., $10^1=10$, $10^2=100$, $10^{-1}=0.1$).10, 1000, 0.01 ExponentA small number written above and to the right of a base number, indicating how many times the base number is multiplied by itself (or divided, if negative).In $10^3$, 3 is the exponent, meaning $10 imes 10 imes 10$. Place ValueThe value of a digit based on its position in a number (e.g., ones, tens, tenths, hundredths).In 3.14, the '1' is in the tenths place, and the '4' is in the hundredths place. Decimal PointThe symbol used to separate the whole number part from the fractional part...

Multiplying by Powers of Ten (10, 100, 1000...) To multiply a decimal by 10, 100, 1000, etc., move the decimal point to the **right** by the number of zeros in the power of ten. This makes the number larger. For example, multiplying by 100 (which has two zeros) means moving the decimal two places to the right. Dividing by Powers of Ten (10, 100, 1000...) To divide a decimal by 10, 100, 1000, etc., move the decimal point to the **left** by the number of zeros in the power of ten. This makes the number smaller. For example, dividing by 1000 (which has three zeros) means moving the decimal three places to the left. Multiplying by Decimal Powers of Ten (0.1, 0.01, 0.001...) To multiply a decimal by 0.1, 0.01, 0.001, etc., move the decimal point to the **left** by the numbe...