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In the United States, both the U. In most other countries, the metric system is the primary system of measurement. If you travel to other countries, you will see that road s list distances in kilometers and milk is sold in liters.
These measurement units are part of the metric system. Unlike the U. For example, a liter is 10 times larger than a deciliter, and a centigram is 10 times larger than a milligram. So, what if you have to find out how many milligrams are in a decigram? Or, what if you want to convert meters to kilometers? Understanding how the metric system works is a good start.
In this section we will discover the basic units used in the metric system, and show how to convert between them. We will also explore temperature scales. In the United States, temperatures are usually measured using the Fahrenheit scale, while most countries that use the metric system use the Celsius scale to record temperatures. The metric system uses units such as meterliterand gram to measure length, liquid volume, and mass, just as the U.
In addition to the difference in the basic units, the metric system is based on 10s, and different measures for length include kilometer, meter, decimeter, centimeter, and millimeter. The metric system also applies the idea that units within the system get larger or smaller by a power of This means that a meter is times larger than a centimeter, and a kilogram is 1, times heavier than a gram. You will explore this idea a bit later. The table below shows the basic units of the metric system. Note that the names of all metric units follow from these three basic units.
In the metric system, the basic unit of length is the meter. A meter is slightly larger than a yardstick, or just over three feet. Among scientists, one gram is defined as the mass of water that would fill a 1-centimeter cube. Weight is a measure of the pull of gravity on an object. Though it is rarely necessary to convert between the customary and metric systems, sometimes it helps to have a mental image of how large or small some units are.
The table below shows the relationship between some common units in both systems. The metric system is a base 10 system. This means that each successive unit is 10 times larger than the one. The names of metric units are formed by adding a prefix to the basic unit of measurement. To tell how large or small a unit is, you look at the prefix. To tell whether the unit is measuring length, mass, or volume, you look at the base. Here is a similar table that just shows the metric units of measurement for mass, along with their size relative to 1 gram the base unit.
The common abbreviations for these metric units have been included as well. The prefixes have the same meanings whether they are attached to the units of length metermass gramor volume liter. Which of the following sets of three units are all metric measurements of length? All of these measurements are from the metric system. For instance, you can figure out how many centigrams are in one dekagram by using the table above. One dekagram is larger than one centigram, so you expect that one dekagram will equal many centigrams.
In the table, each unit is 10 times larger than the one to its immediate right. One gram is 1, times larger than a milligram, so you can move the decimal point in 3, three places to the left. Kilometers km are larger than centimeters cmso you expect there to be less than one km in a cm.
Once you begin to understand the metric system, you can use a shortcut to convert among different metric units. The size of metric units increases tenfold as you go up the metric scale. The decimal system works the same way: a tenth is 10 times larger than a hundredth; a hundredth is 10 times larger than a thousandth, etc.
By applying what you know about decimals to the metric system, converting among units is as simple as moving decimal points. Here is the first problem from above: How many milligrams are in one decigram? You can recreate the order of the metric units as shown below:. This question asks you to start with 1 decigram and convert that to milligrams. As shown above, milligrams is two places to the right of decigrams.
The same method works when you are converting from a smaller to a larger unit, as in the problem: Convert 1 centimeter to kilometers. There are 10 milliliters in a centiliter, 10 centiliters in a Is a kg bigger than a mg, and 10 deciliters in a liter. You used this method when you were converting measurement units within the U. The factor label method works the same in the metric system; it relies on the use of unit fractions and the cancelling of intermediate units.
The table below shows some of the unit equivalents and unit fractions for length in the metric system. You should notice that all of the unit fractions contain a factor of Remember that the metric system is based on the notion that each unit is 10 times larger than the one that came before it. Also, notice that two new prefixes have been added here: mega- which is very big and micro- which is very small. When applying the factor label method in the metric system, be sure to check that you are not skipping over any intermediate units of measurement!
Using the factor label method, write 7, cm as a fraction and use unit fractions to convert it to m. If you have a prescription for 5, mg of medicine, and upon getting it filled, the dosage re 5g of medicine, did the pharmacist make a mistake? Learning how to solve real-world problems using metric conversions is as important as learning how to do the conversions themselves.
Mathematicians, scientists, nurses, and even athletes are often confronted with situations where they are presented with information using metric measurements, and must then make informed decisions based on that data. The first step in solving any real-world problem is to understand its context.
This will help you figure out what kinds of solutions are reasonable and the problem itself may give you clues about what types of conversions are necessary. Here is an example. Marcus bought at 2 meter board, and cut off a piece 1 meter and 35 cm long. How much board is left? Start by calculating how much water will be used in a week using the factor label method to convert the time units. This problem asked for the difference between two quantities. The easiest way to find this is to convert one quantity so that both quantities are measured in the same unit, and then subtract one from the other.
A bread recipe calls for g of flour. How many kilograms of flour would you need to make 5 loaves? Sometimes it is a good idea to check your conversions using a second method. This usually helps you catch any errors that you may make, such as using the wrong unit fractions or moving the decimal point the wrong way. A bottle contains 1. How many mL servings can be made from that bottle?
To answer the question, you will need to divide 1. To do this, convert both to the same unit. You could convert either measurement. Understanding the context of real-life application problems is important. Look for words within the problem that help you identify what operations are needed, and then apply the correct unit conversions. The metric system is an alternative system of measurement used in most countries, as well as in the United States.
The metric system is based on ing one of a series of prefixes, including kilo- hecto- deka- deci- centi- and milli- with a base unit Is a kg bigger than a mg measurement, such as meter, liter, or gram.
Units in the metric system are all related by a power of 10, which means that each successive unit is 10 times larger than the one. This makes converting one metric measurement to another a straightforward process, and is often as simple as moving a decimal point. It is always important, though, to consider the direction of the conversion.
If you are converting a smaller unit to a larger unit, then the decimal point has to move to the left making your smaller ; if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right making your larger. The factor label method can also be applied to conversions within the metric system. To use the factor label method, you multiply the original measurement by unit fractions; this allows you to represent the original measurement in a different measurement unit.
If you have been to other countries, though, you may notice that meteorologists measure heat and cold differently outside of the United States. The difference is that the two countries use different temperature scales. A temperature of. Celsius Fahrenheit. A cook puts a thermometer into a pot of water to see how hot it is. Which temperature scale is the thermometer measuring? By looking at the two thermometers shown, you can make some general comparisons between the scales. Sometimes, it is necessary to convert a Celsius measurement to its exact Fahrenheit measurement or vice versa.
For example, what if you want to know the temperature of your child in Fahrenheit, and the only thermometer you have measures temperature in Celsius measurement? Converting temperature between the systems is a straightforward process as long as you use the formulas provided below. How were these formulas developed? They came from comparing the two scales. Notice how these fractions are used in the conversion formulas. What temperature does water boil at in the Fahrenheit scale? A Celsius temperature is given. To convert it to the Fahrenheit scale, use the formula at the left. A Fahrenheit temperature is given.
To convert it to the Celsius scale, use the formula at the left. The next example shows how these formulas can be used to solve a real-world problem using different temperature scales. Two scientists are doing an experiment deed to identify the boiling point of an unknown liquid.
Which temperature is higher and by how much? To find the difference between them, we need to measure them on the same scale. Whichever way you choose, it is important to compare the temperature measurements within the same scale, and to apply the conversion formulas accurately. What is the average temperature in degrees Fahrenheit? Temperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. You can use conversion formulas to convert a measurement made in one scale to Is a kg bigger than a mg other scale.
Module 3: Measurement. Search for:. Learning Objectives In this lesson you will learn how to do the following: Describe the general relationship between the U. Convert from one temperature scale to the other, using conversion formulas. Try It Now Which of the following sets of three units are all metric measurements of length?
A inch, foot, yard B kilometer, centimeter, millimeter C kilogram, gram, centigram D kilometer, foot, decimeter Show Answer B kilometer, centimeter, millimeter All of these measurements are from the metric system. Example How many milligrams are in one decigram? Show Answer Identify locations of milligrams and decigrams. Dg is 10 times larger than a cg, and a cg is 10 times larger than a mg. Try It Now Convert 3, milligrams to grams. Show Answer One gram is 1, times larger than a milligram, so you can move the decimal point in 3, three places to the left.
Example Convert 1 centimeter to kilometers. Show Answer Identify locations of kilometers and centimeters.Is a kg bigger than a mg
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Whats bigger gram or kilogram?