What are decimals? We explain what decimals are and how the concept is explained to primary-school children, as well as how they are taught to relate decimals to money and measurement, the equivalence between fractions and decimals, partitioning, rounding and ordering decimals and adding, subtracting, multiplying and dividing decimals.
Login or Register to add to your saved resources. A decimal is a number expressed in the scale of tens. Commonly speaking we talk about decimals when numbers include a decimal point to represent a whole number plus a fraction of a whole number tenths, hundredths, etc. A decimal point is a point or dot used to separate the whole part of a number from the fractional part of a number.
Download FREE resources today. For example, the basic unit of time, the day, was divided into hours and then into minutes and then into seconds. Gradually people agreed that there would be 24 hours in a day and that the hours would be of equal length. The hour itself was divided into 60 minutes, which were again divided into 60 seconds. Today even smaller units of time are often needed, for example to describe the race times of runners and swimmers or to keep communications through computers synchronized.
Measuring more and more precisely by creating smaller and smaller units has the advantage that only whole number arithmetic is needed. However, smaller and smaller units need to be invented and the conversions remembered. The metric system makes this easier, with all conversion factors based on ten. The second solution to the problem of describing measuring more precisely is by extending the number system itself to include both common fractions and decimal fractions referred to in this resource as decimals.
Using fractions or decimals, continuous quantities can be described to any desired accuracy:. Note that there are two units the dollar and the cent being used in the money example, but not in the area example. The area example shows that there is no need for the smaller unit the tenth of a square metre to have a name: the number system itself provides all the information required, because the whole number and fractional parts are not separate, but are together in the one number.
There are mathematical advantages to extending the number system rather than creating smaller units. This is not shown with addition and subtraction but with multiplication and division. In the table below, the addition problem can be solved equally easily by thinking about dollars and cents as two linked different units or by thinking of the quantity as one decimal number. However, the multiplication is very hard to do in the first way, but easy in the second.
How much to get both? How to multiply 40 dollars and 35 cents by 36 sq. For example, 34, , etc. Read the whole number part followed by "and", then read the fractional part in the same way as we read whole numbers but followed by the place value of the last digit. The decimal number is always read as individual digits.
As an example, we would read a decimal number of Every Integer can be represented in the form of Decimals, for example, By default, an integer can be considered as a decimal. For performing arithmetic operations involving integers and decimals, the integers are to be converted as fractions. For the addition of 4 to 3. Decimals are used to make our calculations easy. We use them to quickly compare fractions without doing many calculations.
We also use them to shorten the complicated fractional equations. We use decimals every day while dealing with money, weight, length, etc. Decimal numbers are also used in situations where more precision is required which whole numbers cannot provide. To round a decimal number look at the next digit to the right side of the place up to which we want to round off. If the digit is less than 5, round down to the previous number and if the digit is 5 or more than 5, round up to the next higher number.
The decimal 3. Decimals are used to express the whole number and fraction in a single notation. In decimals, whole numbers and fractions are separated by a point known as a decimal point. For example, In Here multiply the numerator and the denominator with a 25, to obtain a in the denominator.
Further, we need to convert this fraction with a denominator of , as a decimal. Learn Practice Download. What are Decimals? Writing Decimals 3. Rounding Decimals to the Nearest Tenth 4. Comparing Decimals 5. Types of Decimals 6. Rounding Decimals to the Nearest Tenth. Types of Decimals Decimals can be divided into different categories depending upon what type of digits occur after the decimal point.
Terminating decimals : Terminating decimals mean it does not reoccur and end after a finite number of decimal places.
For example: Non-terminating decimals : It means that the decimal numbers have infinite digits after the decimal point. For example, The Non-Terminating decimal numbers can be further be divided into 2 parts: Recurring decimal numbers: In Recurring Decimal Numbers, digits repeat after a fixed interval. For example Decimal Related Topics.
Whole Numbers.
0コメント