Dividing by Powers of 10: Simple Tricks

Welcome to understanding powers of ten! This fundamental concept will help us with division later.Let's start with our base number, ten.When we raise ten to different powers, we create larger numbers by adding zeros.Ten to the first power is simply ten, with one zero.Ten squared, or ten to the second power, is one hundred, with two zeros.Ten cubed gives us one thousand, adding a third zero.And ten to the fourth power is ten thousand, with four zeros.Let's understand the pattern that makes powers of ten special.Each time we increase the power by one, we add another zero to our number.The position of each digit determines its value based on its place.This pattern continues infinitely, allowing us to represent very large numbers.Let's look at how these powers relate to our place value system.Each position represents a different power of ten, from right to left.The ones place is ten to the zero power, tens is ten to the first, hundreds is ten squared, and thousands is ten cubed.Now that we understand powers of ten, let's learn a shortcut for dividing by them.Let's start with four hundred and fifty-six divided by one hundred.One hundred has two zeros, so we'll move the decimal point two places to the left.This gives us four point five six.Let's try a bigger number: seven hundred and eighty-nine divided by one thousand.One thousand has three zeros, so we'll move the decimal point three places to the left.This gives us zero point seven eight nine.The key is to remember: just count the zeros in your divisor, and move the decimal point that many places to the left.When dividing by powers of 10, we sometimes need to handle special cases.Let's start with dividing 5 by 100. First, we add a decimal point after the 5.Since we're dividing by 100, which has two zeros, we need to add a leading zero.Now we can move the decimal point two places to the left, giving us 0.05.Let's look at another case where we start with a decimal number, like 45.6 divided by 10.The same rule applies - we move the decimal point one place left, since we're dividing by 10.Let's review the different special cases we might encounter.When working with decimal numbers, the process remains the same.For very small numbers divided by large powers of 10, we may need multiple leading zeros.Here are some examples to practice with. Pause the video and try solving them using what we've learned.Remember, no matter what number you're dividing, the key is to count the zeros and move the decimal point that many places left.